MATLAB Part 2. This week we will look at techniques which will allow you to build powerful applications in MATLAB

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1 MATLAB Part 2 This week we will look at techniques which will allow you to build powerful applications in MATLAB Using M-files for calculations Decisions and loops Introduction to plotting data Start MATLAB and change the working directory to H: Open your workspace Week1.mat from last week. Go to the MATLAB command window and type whos and make sure you still have the Flows and Concs matrices from last week. Using M-files for calculations A computer program usually consists of a number of commands. Except for very small programs, these commands are divided into a series of files. This is to keep the program tidy and to allow it to be modified and used efficiently (just like any other filing system). For example, in Fortran 90, the files are.f90 files. In MATLAB these files are called M- files. There are two types script M-files and function M-files. Script M-files Script M-files are simply a series of lines of text which MATLAB interprets as commands. For example, a script which synthesises and saves the same type of random data that you did last week is shown below: Create a notepad file with this script and save it as rain.m in the working directory. Then run the script by typing the filename in the command window: >>rain Note that all calculated variables are displayed in the command window (unless you include a ; at the end of each line of the script).

2 Script exercise 1 Download (by right-clicking) the file LoadCalcS.M from the web-page and save it on your H:. This is a script M-file which performs the load calculations for the Charles River. Open it using the MATLAB Menu option File Open. MATLAB opens the file using its own M-file editor. You should see; % Multiplies an array of flows by an array of concentrations to obtain an % array of loading rates % unit conversion FlowsConverted = Flows * 24 * 3600; ConcsConverted = Concs / 1000; % calculate load at each source for each day Loads = FlowsConverted.* ConcsConverted; % total all sources for each day TotalLoads = sum(loads') In MATLAB (data files, M-files and the command window) the % sign at the start of a line means the line is a comment which is ignored when you execute your program. It is important to include comments so that everyone can understand your program. Run the script by typing the M-file name in the command window. If you receive a redtype error in the Command window, then check the following; Are matrices Flows and Concs in your workspace? If not, you will have to import them as they are essential for the calculation. Are Flows and Concs named exactly as that (remember MATLAB is case sensitive). Are Flows and Concs in the correct format (numeric matrices of 7 columns and 3 rows)? Have you saved LoadCalcS.M in the same folder as your Workspace? Note 1) only the TotalLoads are displayed in the command window (because of the use of the ; in the script) but all variables have been stored in the workspace, 2) the first two lines are recognised by Matlab as a help facility - try typing help LoadCalcS in the command window. Script exercise 2 In your matrix Loads (which was produced by the LoadCalcS script) you should have a total of 21 items of COD pollution load data. Write a script M-file which; Converts the matrix into a single column vector (revise from the help page Concatenation)

3 Calculates the maximum and minimum of the 21 items (use the max and min functions). Counts the number of items which are greater than 150kg/day (use the find and numel commands). TIPS: 1. Create a new M-file using the File menu, New, M-File and save it as LoadStats 2. Before writing the M-file, you can type your individual commands in the command window, to check that they work. 3. You can find out about the find and numel commands by typing help find and help numel in the command window. 4. The answer is MaxL = 943.5; MinL = 6.7; NumL = Ask a tutor if you need some help! Function M-files Function M-files are slightly different from scripts because inputs and/or output variables are specified in the first line of the M-file. Download (by right-clicking) the file LoadCalcF.M from the web-page and save it on your H:. Open it using the MATLAB Menu option File Open. This Function M-file performs the same calculations as the script you looked at previously. % Multiplies an array of flows by an array of concentrations to obtain an % array of loading rates function [Loads, TotalLoads] = LoadCalcF(Flows, Concs) % unit conversion FlowsConverted = Flows * 24 * 3600; ConcsConverted = Concs / 1000; % calculate load at each source for each day Loads = FlowsConverted.* ConcsConverted; % total all sources for each day TotalLoads = sum(loads'); Type in the MATLAB command window >>[Loads, TotalLoads] = LoadCalcF(Flows, Concs) MATLAB sends the input variables (Flows, Concs) to the Function M-file, does the calculations within the M-File and sends back the output variables [Loads, TotalLoads], which should be listed in the Command window.

4 Why use function M-files rather than script M-files? Often, scripts are adequate. But if you want to have maximum flexibility over inputs and outputs then functions can be better. For example, you could use a different set of inputs (Flows2, Concs2) and outputs [Loads2, TotalLoads2], and your function would still work. Try it by making up new Flows2 and Concs2 and re-running the function: >>Flows2 = Flows * 2 >>Concs2 = Concs * 2 >>[Loads2, TotalLoads2] = LoadCalcF(Flows2, Concs2) On the other hand, using the script, you would have to edit the script - not very convenient when you have many sets of input-output data to analyse, and not possible if you want to create user-friendly applications. Decisions and Loops Almost all computer programs used for engineering and hydrological purposes contain decisions and loops. For example, in a wastewater treatment plant there are usually gas sensors which give an alarm IF the gas concentration exceeds a safe level. Furthermore, the control system may have to continually LOOP through all the sensors in the plant checking for alarms. The MATLAB functions for making decisions are if, elseif and else and for loops, while or for. Using the MATLAB help index (see below) find and study the first Function Reference Pages entitled if and for. Then read the first help page describing the loop function while.

5 Example Sensor_alarm.m (on web-site) is a Function M-File which loops through a data matrix called Sensor_Data, which contains readings from a number of gas sensors (Number_of_S), and reports if the gas concentration found by the sensors is low (L), high (H) or critically high (C). Try to understand the significance of the for, if and else statements: function[warn] = Sensor_alarm(Sensor_Data, Crit_Levels, Number_of_S) LOOP for s = 1:Number_of_S if Sensor_Data(s) > Crit_Levels(s) Warn(s) = 'C'; elseif Sensor_Data(s) > Crit_Levels(s)/2 Warn(s) = 'H'; else Warn(s) = 'L'; end end D E C I S I O N For example, run the function using the following inputs: by typing >>Number_of_S=3 >>Crit_Levels=[ ] >>Sensor_Data=[ ] >>[Warn] = Sensor_alarm(Sensor_Data, Crit_Levels, Number_of_S) The output of the program =should be: Warn = CLH TIPS MATLAB is designed so that the need for loops is minimised. If you have used other programming languages such as Fortran or Visual Basic you will be used to using loops for calculations with arrays. In MATLAB you can usually use matrix functions instead. When using the while function, be careful to not to create an infinite loop, which MATLAB keeps going round and round without being able to finish. If this does happen, you can cancel the whole function by hitting Ctrl-C on your keyboard.

6 Exercise 4 This exercise will apply a while loop and a decision. It also introduces you to plotting data in MATLAB. A river flow routing model is, Q out (k) = a Q (k m) + b Q in out (k 1) where Q out (k) is the downstream flow at time k. Q out (k-1) is the downstream flow at time k-1 (one time-step before k). Q in (k-m) is the upstream flow at time k-m. m is an integer representing a time-delay (the time at which the output begins to respond to the input) which depends upon the properties of the river. a and b are parameters which also depend upon the properties of the river. This model can be used to forecast Q out at the downstream section of the river, and give warning of flooding. Note: 1) to use the model we need to know Q in at all times and have at least one initial value for Q out ; 2) the first forecast of Q out (k) that we can possibly make is at time m after the first measurement of Q in ; 3) We need to calibrate the model in order to find suitable values of the a and b parameters. The following plot shows the measured upstream (Abbeystead) flow and downstream flow (St Michael s) data for a flood on the River Wyre in Northern England. This data is contained within the textfile Wyre.txt which you can download from the web-site. Look at this file using Notepad. Note that the first line of text is preceded by % so that MATLAB will recognise it as a comment, and will not read it.

7 1. Create a matrix Pars which contains the parameters a, b. For now, assume that a = 1 and b = 1. >>Pars = [1 1] 2. Write a function M-file called Routing.M which, - reads the Wyre data text file - runs the model to estimate Q out as a function of Q in every hour for t = 3 to 30 hours. - plots a time-series of the forecast Q out, together with the data for Q out and the data for Q in, - gives a warning if the forecast flood exceeds 100m 3 /s Your only input variable is the matrix Pars. See TIPS and M-file on the next page. 3. Run the model a few times with different values of a and b so that the forecast Q out more closely matches the Q out data. TIPS: Create a new M-file using File New M-file. Save it as Routing You may copy the M-file on the next page. Run the model >> Routing(Pars) When you have finished, save your workspace as Week2.mat >> save Week2

8 Also, keep your Wyre.txt and Routing.M files you will use them next week.