![User-defined Functions
• Some comments about the function declaration
function [x, y, z] = funName(in1, in2)
Must have the reserved
word: function
Function name should
match m-file name
If more than one output,
must be in brackets
Inputs
• No need for return: MATLAB 'returns' the variables whose
names match those in the function declaration (though, you
can use SFUVSO to break and go back to invoking function)
• Variable scope: Any variable created within the function but
not returned disappears after the function stops running
(They’re called “local variables”)
8](https://image.slidesharecdn.com/malabprogramming-240411183944-bfb366a3/85/malab-programming-power-point-presentation-8-320.jpg)
![Functions: overloading
• We're familiar with
» [FSPT
» TJ[F
» MFOHUI
» TVN
• Look at the help file for size by typing
» IFMQTJ[F
• The help file describes several ways to invoke the function
➢ D = SIZE(X)
➢ [M,N] = SIZE(X)
➢ [M1,M2,M3,...,MN] = SIZE(X)
➢ M = SIZE(X,DIM)
9](https://image.slidesharecdn.com/malabprogramming-240411183944-bfb366a3/85/malab-programming-power-point-presentation-9-320.jpg)
![Functions: Exercise
• Write a function with the following declaration:
GVODUJPOQMPU4JO G
• In the function, plot a sine wave with frequency f1, on the
In the function, plot a sine wave with frequency f1, on the
In the function, plot a sine wave with frequency f1, on the
interval [0,2π]:
• To get good sampling, use 16 points per period.
11](https://image.slidesharecdn.com/malabprogramming-240411183944-bfb366a3/85/malab-programming-power-point-presentation-11-320.jpg)
![Line and Marker Options
• Everything on a line can be customized
» QMPU Y Z hTh h-JOF8JEUIh
h$PMPSh
h.BSLFSEHF$PMPSh hLh
h.BSLFS'BDF$PMPSh hHh
h.BSLFS4J[Fh
• See doc line_props for a full list of
properties that can be specified
for a full list of
for a full list of
You can set colors by using
a vector of [R G B] values or
a predefined color character
like 'g', 'k', etc.
h$PMPSh
h.BSLFSEHF$PMPSh hLh
h.BSLFSEHF$PMPSh hLh
h.BSLFS'BDF$PMPSh hHh
h.BSLFS4J[Fh
You can set colors by using
21](https://image.slidesharecdn.com/malabprogramming-240411183944-bfb366a3/85/malab-programming-power-point-presentation-21-320.jpg)
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- 1. Lecture 2: Visualization and Programming 6.057 Introduction to programming in MATLAB Orhan Celiker IAP 2019 1
- 2. Homework 1 Recap Some things that came up: • Plotting a straight line » Y » QMPU Y ➢ Not an error, but probably not what you meant • Use of semicolon – never required if one command per line. You can also put multiple commands on one line; in this case, a semicolon is necessary to separate commands: » YZ Y ?[Y Z 2
- 3. Plotting • Example » YMJOTQBDF QJ » ZTJO Y • Plot values against their index » QMPU Z • Usually we want to plot y versus x » QMPU Y Z MATLAB makes visualizing data fun and easy! 3
- 4. What does plot do? • plot generates dots at each (x,y) pair and then connects the dots with a line • To make plot of a function look smoother, evaluate at more points » YMJOTQBDF QJ » QMPU Y TJO Y • x and y vectors must be same size or else you’ll get an error » QMPU ➢ error!! 10 x values: 1000 x values: 10 x values: 10 x values: 10 x values: 1000 x values: 1000 x values: 1000 x values: 4
- 5. Exercise: Plotting Plot the learning trajectory • In helloWorld.m, open a new figure (use GJHVSF) • Plot knowledge trajectory using U7FD and LOPXMFEHF7FD • When plotting, convert U7FDto days by using TFD1FS%BZ • Zoom in on the plot to verify that IBMG5JNF was calculated correctly 5
- 6. Outline for Lec 2 (1) Functions (2) Flow Control (3) Line Plots (4) Image/Surface Plots (5) Efficient Codes (6) Debugging 6
- 7. User-defined Functions • Functions look exactly like scripts, but for ONE difference ➢ Functions must have a function declaration Help file Function declaration Inputs Inputs Outputs 7 .5-#WFSTJPO$PVSUFTZPG5IF.BUI8PSLT *OD6TFEXJUIQFSNJTTJPO.5-#BOE4JNVMJOLBSFSFHJTUFSFEUSBEFNBSLTPG5IF.BUI8PSLT *OD4FF XXXNBUIXPSLTDPNUSBEFNBSLTGPSBMJTUPGBEEJUJPOBMUSBEFNBSLT0UIFSQSPEVDUPSCSBOEOBNFTNBZCFUSBEFNBSLTPSSFHJTUFSFEUSBEFNBSLTPGUIFJSSFTQFDUJWFIPMEFST
- 8. User-defined Functions • Some comments about the function declaration function [x, y, z] = funName(in1, in2) Must have the reserved word: function Function name should match m-file name If more than one output, must be in brackets Inputs • No need for return: MATLAB 'returns' the variables whose names match those in the function declaration (though, you can use SFUVSO to break and go back to invoking function) • Variable scope: Any variable created within the function but not returned disappears after the function stops running (They’re called “local variables”) 8
- 9. Functions: overloading • We're familiar with » [FSPT » TJ[F » MFOHUI » TVN • Look at the help file for size by typing » IFMQTJ[F • The help file describes several ways to invoke the function ➢ D = SIZE(X) ➢ [M,N] = SIZE(X) ➢ [M1,M2,M3,...,MN] = SIZE(X) ➢ M = SIZE(X,DIM) 9
- 10. Functions: overloading • MATLAB functions are generally overloaded ➢ Can take a variable number of inputs ➢ Can return a variable number of outputs • What would the following commands return: » B[FSPT OEJNFOTJPOBMNBUSJDFTBSF0, » %TJ[F B » N OTJ[F B » Y Z [TJ[F B » NTJ[F B • You can overload your own functions by having variable number of input and output arguments (see WBSBSHJO, OBSHJO, WBSBSHPVU, OBSHPVU) 10
- 11. Functions: Exercise • Write a function with the following declaration: GVODUJPOQMPU4JO G • In the function, plot a sine wave with frequency f1, on the In the function, plot a sine wave with frequency f1, on the In the function, plot a sine wave with frequency f1, on the interval [0,2π]: • To get good sampling, use 16 points per period. 11
- 12. Outline (1) Functions (2) Flow Control (3) Line Plots (4) Image/Surface Plots (5) Efficient Codes (6) Debugging 12
- 13. Relational Operators • MATLAB uses mostly standard relational operators ➢ equal == ➢ not equal ~= ➢ greater than ➢ less than ➢ greater or equal = ➢ less or equal = • Logical operators elementwise short-circuit (scalars) ➢ And ➢ Or | || ➢ Not ~ ➢ Xor xor ➢ All true all ➢ Any true any • Boolean values: zero is false, nonzero is true • See help . for a detailed list of operators 13
- 14. if/else/elseif • Basic flow-control, common to all languages • MATLAB syntax is somewhat unique IF if cond commands end ELSE if cond commands1 else commands2 end ELSEIF if cond1 commands1 elseif cond2 commands2 else commands3 end Conditional statement: evaluates to true or false commands • No need for parentheses: command blocks are between reserved words • Lots of FMTFJG’s? consider using TXJUDI 14
- 15. for • for loops: use for a known number of iterations • MATLAB syntax: for n=1:100 commands end Loop variable Command block for n=1:100 for n=1:100 for commands end • The loop variable ➢ Is defined as a vector ➢ Is a scalar within the command block ➢ Does not have to have consecutive values (but it's usually cleaner if they're consecutive) • The command block ➢ Anything between the for line and the end 15
- 16. while • The while is like a more general for loop: ➢ No need to know number of iterations WHILE while cond commands end • The command block will execute while the conditional expression is true • Beware of infinite loops! CTRL+C?! • You can use CSFBL to exit a loop 16
- 17. Exercise: Conditionals • Modify your QMPU4JO G function to take two inputs: QMPU4JO G G • If the number of input arguments is 1, execute the plot command you wrote before. Otherwise, display the line h5XPJOQVUTXFSF HJWFOh • Hint: the number of input arguments is stored in the built-in variable OBSHJO 17
- 18. Outline (1) Functions (2) Flow Control (3) Line Plots (4) Image/Surface Plots (5) Efficient Codes (6) Debugging 18
- 19. Plot Options • Can change the line color, marker style, and line style by adding a string argument » QMPU Y Z L color marker line-style • Can plot without connecting the dots by omitting line style argument » QMPU Y Z • Look at help plot for a full list of colors, markers, and line styles 19
- 20. Playing with the Plot to select lines and delete or change properties to zoom in/out to slide the plot around to see all plot tools at once 20 .5-#WFSTJPO$PVSUFTZPG5IF.BUI8PSLT *OD6TFEXJUIQFSNJTTJPO.5-#BOE4JNVMJOLBSFSFHJTUFSFEUSBEFNBSLTPG5IF.BUI8PSLT *OD4FF XXXNBUIXPSLTDPNUSBEFNBSLTGPSBMJTUPGBEEJUJPOBMUSBEFNBSLT0UIFSQSPEVDUPSCSBOEOBNFTNBZCFUSBEFNBSLTPSSFHJTUFSFEUSBEFNBSLTPGUIFJSSFTQFDUJWFIPMEFST
- 21. Line and Marker Options • Everything on a line can be customized » QMPU Y Z hTh h-JOF8JEUIh h$PMPSh h.BSLFSEHF$PMPSh hLh h.BSLFS'BDF$PMPSh hHh h.BSLFS4J[Fh • See doc line_props for a full list of properties that can be specified for a full list of for a full list of You can set colors by using a vector of [R G B] values or a predefined color character like 'g', 'k', etc. h$PMPSh h.BSLFSEHF$PMPSh hLh h.BSLFSEHF$PMPSh hLh h.BSLFS'BDF$PMPSh hHh h.BSLFS4J[Fh You can set colors by using 21
- 22. Cartesian Plots • We have already seen the plot function » YQJQJQJ » ZDPT Y TJO Y FYQ BCT Y » QMPU Y Z hLh • The same syntax applies for semilog and loglog plots » TFNJMPHY Y Z hLh » TFNJMPHZ Z hSh » MPHMPH Y Z • For example: » Y » TFNJMPHZ Y FYQ Y hLh 22 TFNJMPHZ Y FYQ Y hLh TFNJMPHZ Y FYQ Y hLh
- 23. 3D Line Plots • We can plot in 3 dimensions just as easily as in 2D » UJNF QJ » YTJO UJNF » ZDPT UJNF » [UJNF » QMPU Y Z [ hLh h-JOF8JEUIh » [MBCFM h5JNFh 23
- 24. 3D Line Plots • We can plot in 3 dimensions just as easily as in 2D » UJNF QJ » YTJO UJNF » ZDPT UJNF » [UJNF » QMPU Y Z [ hLh h-JOF8JEUIh » [MBCFM h5JNFh • Use tools on figure to rotate it • Can set limits on all 3 axes » YMJN ZMJN [MJN 24
- 25. Axis Modes • Built-in axis modes (see EPDBYJTfor more modes) » BYJTTRVBSF ➢ makes the current axis look like a square box » BYJTUJHIU ➢ fits axes to data » BYJTFRVBM ➢ makes x and y scales the same » BYJTYZ ➢ puts the origin in the lower left corner (default for plots) » BYJTJK ➢ puts the origin in the upper left corner (default for matrices/images) 25
- 26. Multiple Plots in one Figure • To have multiple axes in one figure » TVCQMPU ➢ makes a figure with 2 rows and 3 columns of axes, and activates the first axis for plotting ➢ each axis can have labels, a legend, and a title » TVCQMPU ➢ activates a range of axes and fuses them into one • To close existing figures » DMPTF ➢ closes figures 1 and 3 » DMPTFBMM ➢ closes all figures (useful in scripts) 26
- 27. Copy/Paste Figures • Figures can be pasted into other apps (word, ppt, etc) • Edit→ copy options→ figure copy template ➢ Change font sizes, line properties; presets for word and ppt • Edit→ copy figure to copy figure • Paste into document of interest .5-#WFSTJPO$PVSUFTZPG5IF.BUI8PSLT *OD6TFEXJUIQFSNJTTJPO.5-#BOE4JNVMJOLBSFSFHJTUFSFEUSBEFNBSLTPG5IF.BUI8PSLT *OD4FF XXXNBUIXPSLTDPNUSBEFNBSLTGPSBMJTUPGBEEJUJPOBMUSBEFNBSLT0UIFSQSPEVDUPSCSBOEOBNFTNBZCFUSBEFNBSLTPSSFHJTUFSFEUSBEFNBSLTPGUIFJSSFTQFDUJWFIPMEFST 27
- 28. Saving Figures • Figures can be saved in many formats. The common ones are: .fig preserves all information .bmp uncompressed image .eps high-quality scaleable format .pdf compressed image 28 .5-#WFSTJPO$PVSUFTZPG5IF.BUI8PSLT *OD6TFEXJUIQFSNJTTJPO.5-#BOE4JNVMJOLBSFSFHJTUFSFEUSBEFNBSLTPG5IF.BUI8PSLT *OD4FF XXXNBUIXPSLTDPNUSBEFNBSLTGPSBMJTUPGBEEJUJPOBMUSBEFNBSLT0UIFSQSPEVDUPSCSBOEOBNFTNBZCFUSBEFNBSLTPSSFHJTUFSFEUSBEFNBSLTPGUIFJSSFTQFDUJWFIPMEFST
- 29. Advanced Plotting: Exercise • Modify the plot command in your plotSin function to use squares as markers and a dashed red line of thickness 2 as the line. Set the marker face color to be black (properties are -JOF8JEUI, .BSLFS'BDF$PMPS) • If there are 2 inputs, open a new figure with 2 axes, one on top of the other (not side by side), and plot both frequencies (TVCQMPU) QMPU4JO QMPU4JO 29
- 30. Outline (1) Functions (2) Flow Control (3) Line Plots (4) Image/Surface Plots (5) Efficient Codes (6) Debugging 30
- 31. Visualizing matrices Any matrix can be visualized as an image » NBUSFTIBQF » JNBHFTD NBU » DPMPSCBS imagesc automatically scales the values to span the entire automatically scales the values to span the entire • • colormap • Can set limits for the color axis (analogous to YMJN, ZMJN) » DBYJT 31
- 32. Colormaps • You can change the colormap: » JNBHFTD NBU ➢ default map is parula » DPMPSNBQ HSBZ » DPMPSNBQ DPPM » DPMPSNBQ IPU • See IFMQIPU for a list • Can define custom color-map » NBQ[FSPT » NBQ gray jet cool hot(256) parula NBQ NBQ gray jet cool hot(256) You can change the colormap: You can change the colormap: parula » DPMPSNBQ NBQ 32
- 33. Surface Plots • It is more common to visualize surfaces in 3D • Example: • surf puts vertices at specified points in space x,y,z, and connects all the vertices to make a surface • The vertices can be denoted by matrices X,Y,Z • How can we make these matrices ➢ built-in function: meshgrid 33
- 34. surf • Make the x and y vectors » YQJQJ » ZQJQJ • Use meshgrid to make matrices » 9 :NFTIHSJE Y Z • To get function values, evaluate the matrices » ;TJO 9 DPT : • Plot the surface » TVSG 9 : ; » TVSG Y Z ; *Try typing surf(membrane) Use meshgrid to make matrices 9 :NFTIHSJE Y Z surf(membrane) Use meshgrid to make matrices 9 :NFTIHSJE Y Z surf(membrane) 34
- 35. surf Options • See help surf for more options • There are three types of surface shading » TIBEJOHGBDFUFE » TIBEJOHGMBU » TIBEJOHJOUFSQ • You can also change the colormap » DPMPSNBQ HSBZ faceted flat interp 35 There are three types of surface shading There are three types of surface shading faceted flat interp 35 interp interp interp interp flat flat
- 36. contour • You can make surfaces two-dimensional by using contour » DPOUPVS 9 : ; h-JOF8JEUIh You can make surfaces two-dimensional by using contour DPOUPVS 9 : ; h-JOF8JEUIh ➢ takes same arguments as surf ➢ color indicates height ➢ can modify linestyle properties ➢ can set colormap » IPMEPO » NFTI 9 : ; 36 You can make surfaces two-dimensional by using contour DPOUPVS 9 : ; h-JOF8JEUIh takes same arguments as surf can modify linestyle properties
- 37. Exercise: 3-D Plots If two inputs are given, evaluate the following function: If two inputs are given, evaluate the following function: If two inputs are given, evaluate the following function: • Modify QMPU4JO to do the following: • • y should be just like x, but using f2. (use NFTIHSJE to get the X and Y matrices) • In the top axis of your subplot, display an image of the Z matrix. Display the colorbar and use a IPU colormap. Set the axis to xy (JNBHFTD, DPMPSNBQ, DPMPSCBS, BYJT) • In the bottom axis of the subplot, plot the 3-D surface of Z (TVSG) 37
- 38. Exercise: 3-D Plots QMPU4JO generates this figure 38 QMPU4JO generates this figure 38 QMPU4JO generates this figure QMPU4JO generates this figure
- 39. Specialized Plotting Functions • MATLAB has a lot of specialized plotting functions • polar-to make polar plots » QPMBS QJ DPT QJ • bar-to make bar graphs » CBS SBOE • quiver-to add velocity vectors to a plot » 9 :NFTIHSJE » RVJWFS 9 : SBOE SBOE • stairs-plot piecewise constant functions » TUBJST SBOE • fill-draws and fills a polygon with specified vertices » GJMM hSh • see help on these functions for syntax • doc specgraph – for a complete list 39
- 40. Outline (1) Functions (2) Flow Control (3) Line Plots (4) Image/Surface Plots (5) Efficient codes (6) Debugging 40
- 41. find • find is a very important function ➢ Returns indices of nonzero values ➢ Can simplify code and help avoid loops • Basic syntax: index=find(cond) » YSBOE » JOETGJOE YY JOET contains the indices at which x has values between 0.4 and 0.6. This is what happens: x0.4 returns a vector with 1 where true and 0 where false x0.6 returns a similar vector combines the two vectors using logical and operator find returns the indices of the 1's 41
- 42. Example: Avoiding Loops • Given x= sin(linspace(0,10*pi,100)), how many of the entries are positive? Using a loop and if/else count=0; for n=1:length(x) if x(n)0 count=count+1; end end Being more clever count=length(find(x0)); Is there a better way?! length(x) 100 10,000 100,000 1,000,000 Loop time 0.01 0.1 0.22 1.5 Find time 0 0 0 0.04 • Avoid loops! • Built-in functions will make it faster to write and execute 42
- 43. Vectorization • Avoid loops ➢ This is referred to as vectorization • Vectorized code is more efficient for MATLAB • Use indexing and matrix operations to avoid loops • For instance, to add every two consecutive terms: 43
- 44. Vectorization • Avoid loops ➢ This is referred to as vectorization • Vectorized code is more efficient for MATLAB • Use indexing and matrix operations to avoid loops • For instance, to add every two consecutive terms: » BSBOE » C[FSPT » GPSO » JGO » C O B O » FMTF » C O B O B O » FOE » FOE 44 ➢ Slow and complicated
- 45. Vectorization • Avoid loops ➢ This is referred to as vectorization • Vectorized code is more efficient for MATLAB • Use indexing and matrix operations to avoid loops • For instance, to add every two consecutive terms: » BSBOE » BSBOE » C[FSPT » CB FOE B » GPSO ➢ Efficient and clean. Can » JGO also do this using DPOW » C O B O » FMTF » C O B O B O » FOE » FOE 45 ➢ Slow and complicated
- 46. Preallocation • Avoid variables growing inside a loop • Re-allocation of memory is time consuming • Preallocate the required memory by initializing the array to a default value • For example: » GPSO » SFT7FSZDPNQMFYDBMDVMBUJPO » B O SFT » FOE ➢ Variable B needs to be resized at every loop iteration 46
- 47. Preallocation • Avoid variables growing inside a loop • Re-allocation of memory is time consuming • Preallocate the required memory by initializing the array to a default value • For example: » B[FSPT » GPSO » SFT7FSZDPNQMFYDBMDVMBUJPO » B O SFT » FOE ➢ Variable B is only assigned new values. No new memory is allocated 47
- 48. Outline (1) Functions (2) Flow Control (3) Line Plots (4) Image/Surface Plots (5) Efficient codes (6) Debugging 48
- 49. Display • When debugging functions, use disp to print messages » EJTQ hTUBSUJOHMPPQh » EJTQ hMPPQJTPWFSh ➢ EJTQ prints the given string to the command window • It's also helpful to show variable values » EJTQ hMPPQJUFSBUJPOhOVNTUS O ➢ Sometimes it's easier to just remove some semicolons 49
- 50. Debugging • To use the debugger, set breakpoints ➢ Click on – next to line numbers in m-files ➢ Each red dot that appears is a breakpoint ➢ Run the program ➢ The program pauses when it reaches a breakpoint ➢ Use the command window to probe variables ➢ Use the debugging buttons to control debugger Two breakpoints Where the program is now Clear all breakpoints Step to next Stop execution; exit Toggle breakpoint 50 .5-#WFSTJPO$PVSUFTZPG5IF.BUI8PSLT *OD6TFEXJUIQFSNJTTJPO.5-#BOE4JNVMJOLBSFSFHJTUFSFEUSBEFNBSLTPG5IF.BUI8PSLT *OD4FF XXXNBUIXPSLTDPNUSBEFNBSLTGPSBMJTUPGBEEJUJPOBMUSBEFNBSLT0UIFSQSPEVDUPSCSBOEOBNFTNBZCFUSBEFNBSLTPSSFHJTUFSFEUSBEFNBSLTPGUIFJSSFTQFDUJWFIPMEFST
- 51. Performance Measures • It can be useful to know how long your code takes to run ➢ To predict how long a loop will take ➢ To pinpoint inefficient code • You can time operations using tic/toc: » UJD » .ZTUFSZ » BUPD » .ZTUFSZ » CUPD ➢ tic resets the timer ➢ Each toc returns the current value in seconds ➢ Can have multiple tocs per tic 51
- 52. Performance Measures • Example: Sparse matrices » [FSPT QJ » #TQBSTF » JOW XIBUIBQQFOT » JOW # XIBUBCPVUOPX • If system is sparse, can lead to large memory/time savings » [FSPT QJ » #TQBSTF » $SBOE » UJD=$UPDTMPX » UJD#=$UPDNVDIGBTUFS 52
- 53. Performance Measures • For more complicated programs, use the profiler » QSPGJMFPO ➢ Turns on the profiler. Follow this with function calls » QSPGJMFWJFXFS ➢ Displays gui with stats on how long each subfunction took 53 .5-#WFSTJPO$PVSUFTZPG5IF.BUI8PSLT *OD6TFEXJUIQFSNJTTJPO.5-#BOE4JNVMJOLBSFSFHJTUFSFEUSBEFNBSLTPG5IF.BUI8PSLT *OD4FF XXXNBUIXPSLTDPNUSBEFNBSLTGPSBMJTUPGBEEJUJPOBMUSBEFNBSLT0UIFSQSPEVDUPSCSBOEOBNFTNBZCFUSBEFNBSLTPSSFHJTUFSFEUSBEFNBSLTPGUIFJSSFTQFDUJWFIPMEFST
- 54. End of Lecture 2 (1) Functions (2) Flow Control (3) Line Plots (4) Image/Surface Plots (5) Efficient codes (6) Debugging Vectorization makes coding fun! 54
- 55. MITOpenCourseWare https://ocw.mit.edu 6.057 Introduction to MATLAB IAP 2019 For information about citing these materials or our Terms of Use, visit: https://ocw.mit.edu/terms.