Todays Agenda 1 Introduce Matlab User Functions G

Today's Agenda ● 1 Introduce Matlab User Functions G: commoneng 11021102_2005082 matlabm 10. functions. sxi

What are Functions? ● 2 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 G: commoneng 11021102_2005082 matlabm 10. functions. sxi

Matlab's Built-In Functions: ● Elementary Functions ● Data analysis functions ● Array Operations ● Graphing Functions ● Special Functions ● ● Matrix Operations Polynomial Functions ● Signal Processing Functions ● 3 Numerical Methods G: commoneng 11021102_2005082 matlabm 10. functions. sxi

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) 4 number or variable (input value) MATLAB function G: commoneng 11021102_2005082 matlabm 10. functions. sxi

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 5 G: commoneng 11021102_2005082 matlabm 10. functions. sxi

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 6 G: commoneng 11021102_2005082 matlabm 10. functions. sxi

Generic Function Example function [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 ● 7 G: commoneng 11021102_2005082 matlabm 10. functions. sxi

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; 8 ● output_variables = Asqr ● function_name = square. m ● input_variables = side G: commoneng 11021102_2005082 matlabm 10. functions. sxi

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]) 9 G: commoneng 11021102_2005082 matlabm 10. functions. sxi

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 area of square and area of circle [Asqr]=side. ^2; [Acir]=pi*radius. ^2; 10 G: commoneng 11021102_2005082 matlabm 10. functions. sxi

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 >> [Area 1, Area 2] = square_circle(33, 65) >> [surf_a_sq, surf_a_ci]=square_circle(length, r) 11 G: commoneng 11021102_2005082 matlabm 10. functions. sxi

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 ● 12 x=[1, 2, 3, 4, 5, 6, 7, 8, 9, 10] G: commoneng 11021102_2005082 matlabm 10. functions. sxi

Stepwise Refinement 13 ● 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 2 pi ● Evaluate yi=sin(xi) ● Plot yi versus xi G: commoneng 11021102_2005082 matlabm 10. functions. sxi

Program Modules 14 ● 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 G: commoneng 11021102_2005082 matlabm 10. functions. sxi

As a Team ● ● Read the Glen Canyon Dam problem (LM p. 44) Plan your solution to the Glen Canyon Dam Monitoring Analysis. ● ● 15 Break tasks to modules List Input and Output parameters for each module G: commoneng 11021102_2005082 matlabm 10. functions. sxi

Modules ● 16 Main Program ● flow_stats ● daily_ave ● weekly_ave ● plot_data G: commoneng 11021102_2005082 matlabm 10. functions. sxi

main 17 ● 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 G: commoneng 11021102_2005082 matlabm 10. functions. sxi

flow_stats ● Input: hourly flow vector ● Output: mean hourly flow, median hourly flow, standard deviation of hourly flow ● Tasks: ● 18 Calculate mean, median, standard deviation hourly flow for the entire year G: commoneng 11021102_2005082 matlabm 10. functions. sxi

daily_ave 19 ● Input: hour vector, hourly flow vector ● Output: vector day vector, average daily flow ● Tasks: ● Determine number of days in data set ● Day vector = day of year ● Daily ave = mean (flow hours (a: b) ) G: commoneng 11021102_2005082 matlabm 10. functions. sxi

weekly_ave 20 ● 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) ) G: commoneng 11021102_2005082 matlabm 10. functions. sxi

plot_data 21 ● 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 G: commoneng 11021102_2005082 matlabm 10. functions. sxi

Testing Your Code 22 ● 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 G: commoneng 11021102_2005082 matlabm 10. functions. sxi

Team Homework. . . Due: 13 A ● 23 Glen Canyon Dam Analysis (see handout) G: commoneng 11021102_2005082 matlabm 10. functions. sxi