engr-25 lec-07 sp12 functions-3 handles types

7/30/2019 ENGR-25 Lec-07 Sp12 Functions-3 Handles Types

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[email protected] ENGR-25_Functions-3.ppt1Bruce Mayer, PEEngineering/Math/Physics 25: Computational Methods

Bruce Mayer, PELicensed Electrical & Mechanical Engineer

[email protected]

Engr/Math/Physics 25

Chp3 MATLAB

Functions: Part3


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Learning Goals

Understand the difference Built-In andUser-Defined MATLAB Functions

Write User Defined Functions

Describe Global and Local Variables When to use SUBfunctions as

opposed to NESTED-Functions

Import Data from External Data-Files

As generated, for example, by an

Electronic Data-Acquisition System


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Functions (ReDeaux)

MATLAB Has Two Types of Functions

1. Built-In Functions Provided by the

Softeware

e.g.; max, min, median

2. User-Defined

Functions are .m-files

that can accept InPutArguments/Parameters and

Return OutPut Values


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Function Handle (MATLAB help)

MATLAB functions are written toNAMED files or are produced at the

command line as ANONYMOUS

functions. In either case, a function handle is

used to pass the function as an

input argument to a functionfunction.


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[email protected] ENGR-25_Functions-3.ppt5

Bruce Mayer, PEEngineering/Math/Physics 25: Computational Methods

Function Handles

You can create a function handle to anyfunction by using the at sign, @, before the

function name. You can then name the handle

if you wish, and use the handle to reference

the function. For example, to create a handleto the sine function, you type

>> sine_handle = @sin;

where sine_handle is a user-selectedname for the handle (or NickName).


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Function Handles cont

A common use of a function handle is to passthe function as an argument to another

function. For example, plot sinx over 0 x 6

as follows:

>> plot([0:0.01:6], sine_handle([0:0.01:6]))

The Result


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This is a rather cumbersome way to plot thesine function, but the concept can be

extended to create, say, a general purpose

plotting function that accepts a built-in

function as an input. For example,function p = gen_plot(fcn_handle, interval)

plot(interval, fcn_handle(interval))

Create a handle to

the natural log (ln)

function

Plot over 199

>> ln_handle = @log;>>gen_plot(ln_handle,1:99)


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Can Pass a Function with @ sign handle

>> gen_plot(@sech,0:.02:10)


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Calling Functions

There are four ways to invoke, or call, afunction into action. These are:

1. As a character string identifying the

appropriate function .m-file

2. As a function handle3. As an inline function object

4. As a string expression.

Examples of these ways follow for thefzeroBuilt-in fcn which acts on the user-defined

function parab, which computes y = x2 4


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parab.mGraphed

-5 -4 -3 -2 -1 0 1 2 3 4 5-5

0

5

10

15

20

25

x

parab(x)

xplt = linspace(-5,5);

yplt = parab(xplt)plot(xplt,yplt)gridxlabel('x')ylabel('parab(x)')


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Calling Functions cont

1. As a character stringidentifying the

appropriate function

.m-file, which is

The function may be called as follows, to

compute the zero over the range: 0 x 3

>> [x, value] = fzero('parab', [0 3])

x =2

value =0


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2. As a function handle to an existingfunction .m-file:

>> [z, val0] = fzero(@parab,[0, 3])

3. As an inline function object:>> parab1 = 'x.^2-4';>> parab_inline = inline(parab1);>> [w, val_0] = fzero(parab_inline,[0, 3])

w =2

val_0 =0


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4. As a string expression:>> parab2 = 'x.^2-4';>> [u, zero_u] = fzero(parab2,[0, 3])

Or as>> [u, zero_u] = fzero('x.^2-4',[0, 3])u =

2

zero_u =

0


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The function handle method (method 2) isthe fastest method, followed by method 1.

In addition to speed improvement, another

advantage of using a function handle is that it

provides access to subfunctions, which arenormally not visible outside of their defining

.m-file.

If we give a SubFunction a handle, or nickname,

then we can reach into the function file to

engage the useful SubFcn withOUT using the

main function


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Types of User Defined Fcns

The PRIMARY function is the first function ina .m-file and typically contains the main

program. Following the primary function in

the same file can be any number of

subfunctions, which can serve assubroutines that support the primary function.

That is, .m-files can contain code for more

than one function. Additional functions within

the file are called subfunctions, and these

are only visible to the primary function or to

other subfunctions in the same file.


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PRIMARY Function

Usually the primary function is the ONLYfunction in a .m-file that we can call from

the MATLAB Command Window or from

another.m-file function

You invoke the Primary function using thename of the .m-file in which it is defined.

We normally use the same name for the function

and its file, but if the function name differs from

the file name, you must use the FILE name toinvoke the function.


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ANONYMOUS functions enable creation of asimple function withOUT needing to write a

separate a .m-file for it.

You can construct an anonymous function either

at the MATLAB command line or from withinanother function or script.

Thus, anonymous functions provide a quick

way of making a function from any MATLAB

expression withOUT the need to create,name, and save a file.

More on anonymous fcns in a few slides


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SUBFUNCTIONS are placed in the primary

function and are called by the primary fcn You can use multiple functions within a

single primary function m-file

NESTED functions are functions defined

within another function. They can help to improve the readability of your

program and also give you more flexible access tovariables in the .m-file. Produce Nesting Levels

The difference between nested functionsand subfunctions is that subfunctionsnormally cannot be accessed outside oftheir primary function file


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OVERLOADED functions are functions thatrespond differently to different types of input

arguments. They are similar to overloaded

functions in any object-oriented language.

For example, an overloaded function can becreated to treat integer inputs differently than

inputs of class double (precision).

PRIVATE functions enable you to restrict

access to a function. They can be called onlyfrom a .m-file function in the parent directory

Search PATHs will NOT work.


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Function Function

The term function function is not aseparate function type but refers to any

function that accepts another function

as an input argument, such as thefunction fzero orfminbnd

You can pass a function to another

function using a function handle.


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Anonymous Functions

The syntax for creating an anonymousfunction from an expression is

fhandle = @(arglist) expr

Where

The Term arglist is a comma-separated list of

input arguments to be passed to the function

The Termexpr

is any single, valid MATLAB

expression.


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Anonymous Fcn Unit Vector

Consider a Directionin 3D space defined

by LoA running from

Pt-A to Pt-B with

CoOrds as shown Define DIRECTION

Vector AB

kzz

jyyixxAB

AB

AB

AB

Or using Notation

zzjyixAB ABABAB

BBB zyx ,,

AAA zyx ,,


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Next Calculate theGeometric Length,

AB, of The Direction

Vector AB using

Pythagorus

Normalizing AB toits Length will

produce a vector of

unit Length; i.e., u

222 ABABAB

AB

zyx

LABAB

Now AB has the

same Direction as u,

but a different length

BBB zyx ,,

AAA zyx ,,


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Normalize AB toProduce

222

ABABAB

AB

zyx

kzjyix

AB

AB

L

ABu

thes for this case

mz

mymx

AB

ABAB

30

8040

BBB zyx ,,

AAA zyx ,,

Create MATLABAnonymous Fcn:uV(x, y, z)


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Write Anon Fcn uVcompletely in theCOMMAND Window

Test using

conditions Given atRight

BBB zyx ,,

AAA zyx ,,

Also find Space Anglesby acosd(uAB)


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TWO versions of uV anon fcn>> uV1 = @(delX, delY, delZ) [delX delY delZ]/norm([delX delY delZ])uV1 =

@(delX,delY,delZ)[delX,delY,delZ]/norm([delX,delY,delZ])

>> uVa = uV1(13,-29,17)uVa =

0.3607 -0.8046 0.4717

>> uV2 = @(dx, dy, dz) [dx dy dz]/sqrt(sum(dx^2 + dy^2 + dz^2))uV2 =

@(dx,dy,dz)[dx,dy,dz]/sqrt(sum(dx^2+dy^2+dz^2))>> uVb = uV2(13,-29,17)

uVb =

0.3607 -0.8046 0.4717

>> SpcQ = acosd(uVa)SpcQ =

68.8572 143.5740 61.8568


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@Cos_ln (x) Graphed: 0-2.5

0 1 2 3 4 5 6 7 8-10

-8

-6

-4

-2

0

2

4

6

u

v

>> u = linspace(0, 2.5*pi, 300);

>> v = cos_ln(u);>> xZ = [0,8]; yZ = [0, 0];>> plot(u,v, xZ,yZ, 'LineWidth',3),grid, xlabel('u'), ylabel('v');>> Z1 = fzero(cos_ln,2)Z1 =

1.4429>> Z2 = fzero(cos_ln,5)Z2 =

4.9705>> Z3 = fzero(cos_ln,8)Z3 =

7.5425


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ANONYMOUS Function example

Build, completely in the Command Window,a function that returns the

nth Root of a Scalar Base

nBz 1>> nth_root = @(B,n) B.^(1./n);

>> z = nth_root(31,3)z =3.1414

>> z1 = nth_root(-99,4.3)z1 =

2.1683 + 1.9428i>> nth_root(10, [2:6])ans =

3.1623 2.1544 1.7783 1.5849 1.4678


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Anonymous Functions cont

You can pass the handle of an anonymousfunction to other functions.

For example, to find the minimum of the polynomial

4x2 50x + 5 over the interval [10, 10]

>>poly1 = @(x) 4*x.^2 - 50*x + 5;>>fminbnd(poly1, -10, 10)ans =

6.2500

Omit the Handle for a One-Time fcn usefminbnd(@(x) 4*x.^2 - 50*x + 5, -10, 10)


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Calling One Fcn within Another

One anonymous function can call another toimplement function composition.

Consider the function h(x) = 5sin(x3). It is

composed of the fcns g(y) = 5sin(y)

and y = f(z) = z3 h(x) = g(f(x)) In the following session

the function whose

handle is h calls the

functions whosehandles are f and g.

>>f = @(x) x.^3;>>g = @(x) 5*sin(x);>>h = @(x) g(f(x));

>>h(2)ans =

4.9468


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Variables and Anonymous Fcns

Variables can appear in anonymousfunctions in two ways:

1. As variables specified in the argument list,as for example f = @(x) x.^3;

2. As variables PreDefined in the body of the

expression, as for example with the variablesA and B in plane = @(x,y) A*x + B*y


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Vars & Anonymous-Fcns cont

When the function is created MATLABcaptures the values of these variables and

retains those values for the lifetime of the

function handle.

If the values of A or Bare changed after the

handle is created,

their values associated

with the handle doNOT change.

>> A = 3; B = 7;

>> plane = @(x,y)A*x + B*y>> P1 = plane (1,2)P1 =

17>> A = 9; B = 14;>> P2 = plane (1,2)P2 =

17


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SubFunctions A function .m-file may contain more than one

user-defined function. The first defined function in the file is called the

primary function, whose name is the same as them-file name.

All other functions in the file are calledsubfunctions.

Subfunctions are normally visible only tothe primary function and other subfunctions

in the same file; that is, they normally cannot be called by

programs or functions outside the primary fcn file this limitation can be removed with fcn handles


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SubFunctions cont

Create the primary function first with afunction definition line and its defining code,

and name the .m-file with this function

name as usual.

Next, create within the .m-file eachsubfunction with its own function definition

line and defining code

The orderof the subfunctions does not matter,

but function names must be unique within

the primary function .m-file.


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SubFunction Examplefunction [avg, med] = newstatsSF(u) % Primary function

% Bruce Mayer, PE * 06Feb12 * ENGR25% file = newstatsSF.m (SHOULD match fcn name)% NEWSTATS Find mean and median with internal functions.n = length(u);avg = mean(u, n);med = median(u, n);

function a = mean(v, n) % Subfunction% Calculate average.a = sum(v)/n;

function m = median(v, n) % Subfunction% Calculate median.w = sort(v);if rem(n, 2) == 1m = w((n+1) / 2);

elsem = (w(n/2) + w(n/2+1)) / 2;

end


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SubFunction Example Results

>> w = [12:0.37:209];>> z = log(w).*(cos(w)).^2;>> [zavg, zmed] = newstatsSF(z)

zavg =

2.2590

zmed =

2.1168


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Function-Call Precedence

The order in which MATLAB checks forfunctions is very important. When a function

is called from within an .m-file, MATLAB

1. first checks to see if the function is a built-in

function such as sin.2. Next it checks to see if it is a subfunction

in a primary function .m-file

3. then checks to see if it is a private function

which is a function m-file residing in the PRIVATEsubdirectory of the calling function

4. Then MATLAB checks for normal

.m-files on your search path


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SubFunction Example

This example shows how the MATLABm-function mean can be superceded by our

own definition of the mean, one which gives

the Root-Mean Square (RMS) value.

The function mean is a subfunction. The function residual_x is the primary function.

function r = residual_x(a)r = a - mean(a);%

function w = mean(z)w = sqrt(sum(z.^2))/length(z);


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SubFunction Example cont

Note thatmean

is a std MATLAB .m-File

Suggest checking mean in MATLAB Help

Use RMS residual fcn on [4,-4]

>> v = [ 4 -4];

>> r1 = residual_x(v)r1 =

1.1716 -6.8284

The ReDefined mean

does NOT changethe standard

MATLAB version

>> r2 = v - mean(v)r2 =

4 -4

Note:

RMS mean = 2.8284


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SubFunction Assessment

The use ofsubfunctions enables you toreduce the no. of files that define your fcns

For example, if it were not for the subfunction

mean in the previous example, we would have

had to define a separate .m-file for our meanfunction and give it a different name so as not to

confuse it with the MATLAB fcn of the same name

Subfunctions are normally visible only to the

primary function and other subfunctions inthe same file

However, we can use a function handle to allow

access to the subfunction from outside the m-file


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All Done for Today

Some RootMean Square

Calculations


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Bruce Mayer, PELicensed Electrical & Mechanical Engineer

[email protected]

Engr/Math/Physics 25

Appendix 6972 23 xxxxf


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@Cos_ln (x) Graphed

0 0.5 1 1.5 2 2.5 3-10

-8

-6

-4

-2

0

2

4

6

8

x

y

=

cosln

(x)

cos_ln = @(x) 7*cos(x) - log(x+1)xplt = linspace(0,3);yplt = cos_ln(xplt);

plot(xplt,yplt)gridxlabel('x')ylabel('y = cos_ln(x)')


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Anonymous Fcn Unit Vector>> uV1 = @(delX, delY, delZ) [delX delY

delZ]/(sqrt(sum([delX delY delZ].*[delX delY

delZ])));

>> uVtest1 = uV1(7, -9, 4)

uVtest1 =

0.5793 -0.7448 0.3310

>> uV2 = @(delX, delY, delZ) [delX delY

delZ]/norm([delX delY delZ]);>> uVtest2 = uV2(7, -9, 4)

uVtest2 =

0.5793 -0.7448 0.3310


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Anonymous Fcn Unit Vector thes for this case

Use uv2 to find

mz

mymx

AB

ABAB

30

8040

uT =

-0.4240 0.8480 0.3180

>> SpcAng = acosd(uT)

SpcAng =

115.0873 32.0054 71.4580


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Anonymous Fcns: Multi-Inputs

You can create anonymous functions having

more than one input. For

example, define the function

>> pythag = @(x,y) sqrt(x.^2 + y.^2);

>> c = pythag(13,17)c =

21.4009

>> pythag([3,7],[4,11])ans =

5.0000 13.0384

22 yxpythag

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