LAB 0 MATLAB INTRODUCTION

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1 Befre lab: LAB 0 MATLAB INTRODUCTION It is recmmended that yu d the secnd prblem n the hmewrk befre cming t lab, althugh that wn t be required r cllected in lab. It is als recmmended that yu read the Intrductin t Using MATLAB fr Systems Calculatins. Objectives: 1) Gain prficiency with MATLAB. 2) Becme cmfrtable with the tw things that will cause cnfusin repeatedly thrughut the curse unless yu take the time t understand them thrughly nw: Write-up: a) The differences between different kinds f matrix and vectr multiplicatin in MATLAB. b) The use f functins, functin arguments and functin names. Nne, but all students shuld check with the TA that their functins perate satisfactrily befre they leave the lab. Time allcatin (an apprximate guideline): Intrductin t the lab, including accessing MATLAB fr this lab 15 minutes Part 1. Increase familiarity with MATLAB 1 hur Part 2. Using functins 1 hur Supplementary materials: Using MATLAB fr Systems Calculatins. handut. This prvides further backgrund n MATLAB beynd that in this MATLAB Quick Reference. A list f the mst imprtant cmmands yu ll need fr 22, with very brief descriptins. Intrductin t Unix fr Engs 22. This prvides infrmatin needed t access MATLAB via the UNIX perating system, which is ptinal fr the purpse f ENGS 22. Web resurces, linked frm the Infrmatin n Cmputers and MATLAB sectin f the infrmatin sectin f the ENGS 22 site n (A quick link t the 22 site is 1. Increasing Familiarity with MATLAB Ntes: This handut is nt a cmprehensive tutrial yu will need t read the handut Using MATLAB fr Systems Calculatins as well, and use the MATLAB help functin r n-line dcumentatin. 0. Accessing MATLAB. Starting MATLAB n a Windws Wrkstatin in Lab 222. Step-by-step instructins are n the next page Lab 0 MATLAB Warm-up Page 1

2 Details here may change as they are presently updating the cmputers in 222: Lg in, using the Thayer username and passwrd assigned t yu, NOT yur blitz/dnd name and passwrd. Set the dmain t Lg n t: Cummings. If yu haven t yet, yu ll want t change yur passwrd. The easy way t d that is n the Web at Click the MATLAB Icn n the desktp r Click Start n the taskbar then mve the cursr ver Prgrams n the Start Menu then Matlab6.5 n the Prgrams Menu then Matlab6.5 applicatin in the Matlab 6.5 Menu. 1. Practice using MATLAB as a calculatr. Use a prblem f yur chice, r calculate the number f hurs in a year. Try using the up arrw key t change yur calculatin. 2. Create these vectrs, a = [1, 2, -1], b = [3, -1, 1], c = [0, 1, 1] a) Type a and a t see the vectr a and its transpse. If yu frget whether a vectr is a rw r a clumn, this is a gd quick way t check. b) Try asking MATLAB t perfrm sme calculatins n thse vectrs with the fllwing: a + b, a * b b * a b.* a b * a Make sure the results make sense t yu in particular, understand the difference between the different multiplicatins. See the appendix n visualizing matrix multiplicatin (last page f this dcument) if yu are rusty n hw matrix multiplicatin wrks. Taking the time t understand this nw is well wrth it cnfusin abut these issues will cause yu truble repeatedly in this curse. Yu ll tear ut yur hair again and again. Get ut a pencil and paper and try the calculatins yurself t make sure yu are right abut what MATLAB is ding. If it desn t make sense, dn t g n stp and ask fr help. 3. Because MATLAB is vectr-riented, mst lps can be avided. (a) Plt y = x 2 vs x fr 7 pints between x = 1 and 1, inclusive. This can be accmplished with the fllwing cmmands: x = linspace(-1, 1, 7) y = x.^2 plt(x, y) Nte that.^ raises each element f x t a pwer. (x^2 wuld try t multiply the vectr x by itself, but the dimensins dn t wrk ut if yu d that it wuld need t be x *x r x*x.) It is wrth pausing a mment t recall hw this might be dne in C++: cnst int npts = 7; int n; real x[npts], y[npts], dx; dx = 2.0/(npts-1); x[0] = -1; fr(n=0; n<npts; n++) { x[n] = x[0] + n*dx; y[n] = pw(x[n], 2); } /* And nw yu can insert yur pltting cmmands */ The MATLAB versin is cnsiderably simpler! Lab 0 MATLAB Warm-up Page 2

3 (b) Repeat the plt, but with better reslutin use 100 pints instead f six. Yu can use the up arrw t avid a lt f retyping. Als, yu dn t really want t see all 100 numbers n yur screen. Yu can suppress the screen display f the results f any line by putting a semicln after it. S yur cmmands lk like this: x = linspace(-1, 1, 100); y = x.^2; plt(x, y); 4. Plt the functin y = t e 2t vs. t (t = 0). (Hint: type help exp ). Yu can use much the same apprach as was used abve. Use as many pints as yu need t prduce a satisfactry graph, and select a maximum value fr t which is sufficient t display the mst interesting prtin f the graph. Add axis labels (xlabel, ylabel) and a descriptive title (title), which includes yur name. (Use MATLAB help t find ut mre abut any f these cmmands.) Make a hardcpy f yur graph. 5. Calculate 100 samples each f the functins y 1 = cs(2πft) and y 2 = sin(2πft), where f = 1 Hz and t =.01 sec. (a) (b) (c) Plt these functins vs. t, n the same graph. D it again, but put the tw functins n separate graphs in the same figure windw (use subplt see the ther handuts, r type help subplt). Plt y 2 vs y 1. Use the cmmand axis square t make a square pltting bx. What d yu bserve? Nw yu ll learn hw t create and use an M-file. 6. Smething yu need t calculate ften fr electrical systems is the resistance f a parallel cmbinatin f resistrs. As yu ll see later in the class, this same calculatin is useful fr mechanical, thermal, and fluid systems as well. Fr tw resistrs in parallel, like this: R1 R2 the net resistance is R P = R 1 R 2 R 1 + R 2 Yu culd use MATLAB t calculate this as fllws: % SET UP THE RESISTANCES R1 = 1000; % Resistance in hms R2 = 1200; % CALCULATE THE PARALLEL COMBINATION Rp = R1*R2/(R1+R2); % DISPLAY THE RESULT Rp Type each f these cmmands in the cmmand windw, just t see what happens (Yu can mit the cmments, fr simplicity). Lab 0 MATLAB Warm-up Page 3

4 7. Open the MATLAB editr (by clicking n the blank dcument icn), and create a dcument cntaining the cmmands abve. Name it smething like rpar.m. Details here may change as they are presently updating the cmputers in 222: Save it t a flder n the T drive. The T drive is actually the Thayer netwrk file system. Saving yur wrk n the T drive rather than n any f the lcal drives is imprtant fr several reasns: Yu can then access yur wrk frm any Thayer machine. The lcal drives are cleaned peridically. If yu leave yur wrk n a lcal drive it will get wiped ut with n warning, prbably at an incnvenient time. If yu leave cursewrk n a public machine, yu might get inadvertently mixed up in an Hnr Principle hearing. If smene uses yur wrk, it might nt be clear t the COS wh cpied frm whm.. Nw, if yu type rpar in the MATLAB cmmand windw, yu perfrm this simple calculatin. Hwever, yu have t make sure the MATLAB knws t lk n the T drive fr yur wrk if it desn t, see step 10 n the last page, r ask a TA fr help. Yu can change the values f R1 and R2 in the file, save it again, and run it again t calculate different values. But that s a clumsy way t d it: better is t write a functin. 8. I always used t wish my calculatr had a buttn n it t calculate the parallel cmbinatins f resistrs. Editing the file is ne way t d that, we can make MATLAB much mre like that imaginary calculatr, by creating a parallel resistr functin. T make an M-file int a functin, it needs a line like this: functin utput = f(input1,input2) The italicized wrds are nes that yu replace with yur wn names. f is the name f the functin and shuld be the same as the name f the file that has the functin in it (f.m). There can be any number f inputs (separated by cmmas), and utput is anything yu want t pass back t the calling prgram (r the cmmand windw). See the MATLAB Prgramming sectin f the Using MATLAB fr Systems Calculatins handut fr mre infrmatin and an example. Mdify yur M-file t make it a functin. When yu re dne, yu shuld be able t get the parallel cmbinatin f tw resistrs by typing Rcmb = rpar(800, 500) where 800 and 500 are the tw resistances yu want t cmbine. Yu ve nw gt that functin built int MATLAB! 9. T see hw the variable names wrk, try ding the fllwing in the cmmand windw: x = 800; y = 500; z = rpar(x,y) Ntice that this wrks even thugh yu (presumably) used a different name fr the inputs inside yur functin. Thse variables are lcal, within yur functin. The fact that R1 gets set t x is determined by that being the first variable in the list, nt by the variable name. 10. Nw yu will make a mre sphisticated functin that can calculate the cmbinatin f three resistrs, and can d it either fr resistrs in series r fr resistrs in parallel. Here are sme hints n each aspect f that task. The skills yu will learn in this exercise will be essential fr using the de45 functin yu will be using extensively n the next hmewrk. Lab 0 MATLAB Warm-up Page 4

5 a. Hw t calculate three resistrs in parallel. Yu may knw a frmula fr that, r knw hw t calculate it, but yu dn t need t. Why? Because if we have three resistrs in parallel, and start by cmbining just tw f them in parallel, we will then have tw resistrs in parallel, and we nt nly knw hw t calculate that, but we ve gt a functin t d the wrk fr us. S we can just d smething like: first_tw = rpar( r1, r2 ) all_three_in_parallel = rpar( first_tw, r3 ) Or yu can d it in just ne line: all_three_in_parallel = rpar( rpar( r1, r2), r3); b. T be able t d this with series resistrs t, yu might want t make a series resistr functin, rser.m It culd be fr just tw resistrs. c. Yu ll need t be able t tell yur d-it-all functin whether the resistrs are in series r in parallel. T d this, yu can use ne f yur input arguments t pass the name the functin yu want t use (either rser r rpar). That name is nt a numerical value but a string. In MATLAB, yu can put strings int variables almst the same way yu put numerical values in: f = hell will make the variable f hld the string hell. Then, if yu were t call a functin using the variable f, the string hell wuld get passed int the functin. Fr example, the functin disp will display a variable, s if yu were t type disp(f) r disp( hell ) either ne wuld display the wrd hell. T check yur understanding, see if yu can figure ut what wuld happen if yu typed f = gdbye disp( f ) and see if yu get what yu expect. If yu dn t, check with a TA fr help understanding it. d. Suppse yu have the name f a functin in a variable (e.g. fbar = sin ) and yu want t excecute that functin. If yu just type fbar(pi/4) Matlab will think yu want the π/4 th element f the vectr fbar and will give yu an errr messages. Yu need t tell Matlab t execute the functin named by the string in yur variable. Yu can d that with the built-in MATLAB functin called feval, like this: feval(fbar,pi/4) e. Nw yu shuld have all the pieces yu need t put tgether a functin that will take an input like fancyfunctin( rpar, 500, 600, 700) and calculate the parallel cmbinatin f the three resistrs (r the series cmbinatin if yu use rser as the first argument). Once yu get the functin wrking, demnstrate it t a TA. Lab 0 MATLAB Warm-up Page 5

6 Lab 0 MATLAB Warm-up Page Setting the MATLAB path. (Optinal) The MATLAB search path is a list f directries (flders) where MATLAB lks fr functins. Yu can add ther directries t this path by pening the path brwser ( Set Path under the File menu). This will be useful if yu want t set up mre directries t keep track f different assignments. 13. Quitting (Nt Optinal): 13.1 Exit MATLAB (type exit r select it frm the file menu) 13.2 Lg ff the cmputer t keep yur files n the T: drive safe. Appendix: Visualizing Matrix Multiplicatin I like t write matrix prducts, such as AB = C with the matrices psitined like this: B A C This makes it easy t visually see bth which elements get multiplied, and where they g in the prduct, and it makes it easy t see what size and shape the prduct shuld be. Fr example, t cmpute h g f e d c b a, I write: d c b a h g f e Then sighting hrizntally acrss the matrix n the left shws yu the elements invlved in a given element f the prduct, and sighting vertically dwn the tp matrix shws yu the elements f it that are invlved. + bg ae d c b a h g f e This als allws yu t quickly see that a rw times a clumn gives a scalar: [ ] [ ] and that a clumn times a rw gives a matrix: [ ]

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