engr-25 lec-06 sp12 functions-2 builtin udf (1)

7/30/2019 ENGR-25 Lec-06 Sp12 Functions-2 BuiltIn UDF (1)

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[email protected] ENGR-25_Functions-2.ppt1Bruce Mayer, PEEngineering/Math/Physics 25: Computational Methods

Bruce Mayer, PELicensed Electrical & Mechanical Engineer

[email protected]

Engr/Math/Physics 25

Chp3 MATLAB

Functions: Part2


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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 an External Data-File

As generated, for example, by anElectronic 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, median2. User-Defined

Functions are .m-files

that can accept InPutArguments/Parameters and

Return OutPut Values


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Array Function Operations

MATLAB will treat a variable as anarray automatically.

For example, to compute the

square roots of 7, 11 and 3-5j, type

>> u = [7, 11, (3-5j)]

>> sqrt(u)

ans =2.6458 3.3166 2.1013 - 1.1897i


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[email protected] ENGR-25_Functions-2.ppt5

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

Expressing Fcn Arguments

We can write sin2 in text, but MATLABrequires parentheses surrounding the 2

The 2 is called the fcn argument orparameter

To evaluate sin2 in MATLAB, type sin(2)

The MATLAB function name must be followed by apair of parentheses that enclose the argument

To express in text the sine of the 2nd element

of the array x, we would type sin[x(2)]. However, in MATLAB you cannot use

square brackets or braces in this way,and you must type sin(x(2))


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Expressing Fcn Arguments cont

Evaluate sin(x2

+ 5) type sin(x.^2 + 5) Evaluate sin(x+1) type sin(sqrt(x)+1)

Using a function as an argument of another

function is called function composition.

Check the order of precedence and the numberand placement of parentheses when typing such

expressions

Every left-facing parenthesis requiresa right-facing mate.

However, this condition does NOTguarantee that the expression is CORRECT!


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Expressing Fcn Arguments cont

Another common mistake involvesexpressions like cos2y, which means (cosy)2.

In MATLAB write this expression as(cos(y))^2 or cos(y)^2

Do NOT write the Expression as

cos^2(y)

cos^2y

cos(y^2)

>> cos(pi/1.73)ans =

-0.2427

>> (cos(pi/1.73))^2ans =

0.0589


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Built-In Trig Functions

MATLAB trig fcns operate in radian mode

Thus sin(5) returns the sineof 5 rads, NOT the sine of 5.

Command Conventional Math Functioncos(x) Cosine; cos xcot(x) Cotangent; cot xcsc(x) Cosecant; csc xsec(x) Secant; sec xsin(x) Sine; sin xtan(x) Tangent; tan x

rads

rads

180


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Built-In Inverse-Trig Functions

MATLAB trig-1 fcns also operate in radian mode

i.e., They Return Angles in RADIANS

Command Conventional Math Functionacos(x) Inverse cosine; arccos x.acot(x) Inverse cotangent; arccot x.acsc(x) Inverse cosecant; arccsc xasec(x) Inverse secant; arcsec xasin(x) Inverse sine; arcsin xatan(x) Inverse tangent; arctan x

atan2(y,x) Four-quadrant inverse tangent TwoaTans?


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Why Two aTans?

Consider theSituation at Right(-4,3)(-4,3)(-4,3)

(4,-3)

37

143

87.3675.0arctan

43arctan

87.3675.0arctan

43arctan

x

x

Due to aTan range

/2 y /2


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Why Two aTans? cont

Calculator Confusion from

(-4,3)(-4,3)(-4,3)

(4,-3)

37

143

14343arctan43arctan37

MATLAB Solves This problemwith atan2 which allows input

of the CoOrds to ID the proper Quadant

MATLAB atan>> q1 = atan(-3/4)

q1 =-0.6435>> q2 = atan(3/-4)q2 =

-0.6435

MATLAB atan2>> q3 = atan2(-3,4)

q3 =-0.6435>> q4 = atan2(3,-4)q4 =

2.4981


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atan2 built into Complex angle

As noted in the

Discussion ofComplex numbers

converting between

the RECTANGULAR

& POLAR forms

require that we note

the Range-Limits of

the atan function MATLABs angle

function uses atan2

>> z1 = 4 - 3jz1 =

4.0000 - 3.0000i

>> z2 = -4 + 3jz2 =-4.0000 + 3.0000i

>> r1 = abs(z1)r1 =

5

>> r2 = abs(z2)

r2 =5

>> theta1 = atan2(imag(z1),real(z1))theta1 =

-0.6435

>> theta2 = atan2(imag(z2),real(z2))theta2 =

2.4981

>> z1a = r1 *exp(j *theta1)z1a =

4.0000 - 3.0000i

>> z2b = r2 *exp(j *theta2)z2b =

-4.0000 + 3.0000i


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Degree Trig Functions

MATLAB now has Trig Functions thatOperate on angles in DEGREES ()

Example: Y = cosd()

Where is Measured in Degrees cosd()

sind()

tand()

cotd()

cscd()

secd()

acosd(y)

asind(y)

atand(y)

acotd(y)

acscd(y)

asecd(y)

NOatan2d(y)though

(wellmake one)


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Built-In Hyperbolic Functions

Command

Conventional Math Function

cosh(x) Hyperbolic cosine.coth(x) Hyperbolic cotangentcsch(x) Hyperbolic cosecantsech(x) Hyperbolic secantsinh(x) Hyperbolic sinetanh(x) Hyperbolic tangent


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Built-In Inverse-Hyp Functions

Command Conventional Math Functionacosh(x) Inverse Hyperbolic cosine.acoth(x) Inverse Hyperbolic cotangentacsch(x) Inverse Hyperbolic cosecantasech(x) Inverse Hyperbolic secantasinh(x) Inverse Hyperbolic sineatanh(x) Inverse Hyperbolic tangent

>> asinh(37)ans =

4.3042>> asinh(-37)ans =

-4.3042

>> acosh(37)ans =

4.3039>> acosh(-37)ans =

4.3039 + 3.1416i


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User-Defined Functions (UDFs)

The first line in a function file must begin witha FUNCTION DEFINITION LINE that has a list

ofinputs & outputs.

This line distinguishes a function m-file from a

script m-file. The 1st Line Syntax:function [output variables] = name(input variables)

Note that the OUTPUT variables are enclosed inSQUARE BRACKETS, while the input variables

must be enclosed with parentheses. The function name (here, name) should be the

same as the file name in which it is saved

(with the .m extension).


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UDF Example

The Active m-File Linesfunction ave3 = avg3(a, b, c)TriTot = a+b+c;ave3 = TriTot/3;

Note the use of asemicolon at the end

of the lines. This

prevents the values ofTriTot and ave3

from being displayed


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UDF Example cont

Call this Function with its OutPut Agrument>> TriAve = avg3(7,13,-3)TriAve =

5.6667

To DetermineTriAve the

Function takes

a = 7 b = 13

c = 3


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UDF Example cont

Call the avg3 function withOUT its outputargument and try to access its internal value,avg3. You will see an error message.

>> avg3(-23,19,29)

ans =8.3333

>> ave3??? Undefined function or variable 'ave3'.

The variable ave3 is LOCAL to the UDF

Its Value is NOT defined OutSide the UDF


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UDF Example cont

The variables a, b, & care local to the function

avg3, so unless you pass

their values by naming

them in the commandwindow, their values will

not be available in the

workspace outside the

function. The variable TriTot is

also local to the function.

>> a=-37; b=73; c=19;>> s = avg3(a,b,c);

>> aa =

-37>> b

b =73

>> cc =

19

>> TriTot??? Undefinedfunction or variable'TriTot'.


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UDF 2nd Example

New Function tetf t cos6

Write Function DecayCos with inputs of t &

function ecos = DecayCos(t,w)% Calc the decay of a cosine% Bruce Mayer, PE ENGR25 28Jun05% INPUTS:% t = time (sec)

% w = angular frequency (rads/s)% Calculation section:ePart = exp(t/6);ecos =cos(w.*t)./ePart;

w & t can be

Arrays


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UDF 2nd Example cont

Pass Arrays to DecayCos tetf t cos6

>> p = DecayCos([1:3],[11:13])

p =

0.0037 0.3039 0.1617

Note that in MATLAB [11:13] [11:1:13] = [ 11, 12, 13]


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UDF Multiple Outputs

A function may have more than one output.These are enclosed in square brackets [ ]

The OUPput is on the LEFT-hand side of the =sign in the function definition line

For example, the function Res computes theElectrical Current, Ires, and Power-

Dissipated, Pres, in an

Electrical Resistor

given its Resistance, R,and Voltage-Drop, v,

as input arguments

R

v

i


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UDF Multiple Outputs cont

Calling thefunction Res for

4.7 and 28 V Res has 2-INputs &

2-OUTputs>> [I1 P1] = res(4.7,28)

I1 =5.9574

P1 =166.8085


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Examples of Fcn Def Lines

1. One input, one output:

function [area_square] = square(side)

2. Vector-Brackets are optional for one output:

function area_square = square(side)

3. Three inputs, one output (Brackets Optional):function [volume_box] = box(height,width,length)

4. One input, Two outputs (Vector-Brackets Reqd):

function [area_circle,circumf] = circle(radius)

5. Output can be a Plot as well as number(s)

function sqplot(side)


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Example Free Fall

Consider an objectwith arbitrary mass, m,

falling downward

under the acceleration

of gravity with negligible

air-resistance (drag)

With original

velocity v0

Take DOWN as

POSITIVE direction


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Example Free Fall cont

0

vgttv tvgtddttvdt

0

2

0 2

1

Use NewtonianMechanics to

analyze the Ballistics

of the falling Object

The Velocity andDistance-Traveled

as a function of time

& Original Velocity


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Free Fall/Drop MATLAB Fcn

function [dist, vel] = drop(g, v0, t);% Calc Speed and distance-traveled by% dropped object subject to accel of gravity% Bruce Mayer, PE ENGR25 27Jun05%

% Parameter/Argument List% g = accel of gravity% v0 = velocity at drop point (zero-pt)% t = falling time

%% Calculation section:vel = g*t + v0;dist = 0.5*g*t.^2 + v0*t;


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Calling Function drop

1. The variable names used in the functiondefinition may, but need not, be used when

the function is called:

>> a = 32.17; % ft/s^2

>> v_zero = -17; % ft/s>> tf = 4.3; % s

>> [dist_ft, spd_fps] = drop(a, v_zero, tf)dist_ft =224.3117

spd_fps =121.3310


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Calling Function drop cont

2. The input variables need not be assignedvalues outside the function prior to the

function call:

>> [ft_dist, fps_spd] = drop(32.17, -17, 4.3)

ft_dist =224.3117

fps_spd =

121.3310


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Calling Function drop cont

3. The inputs and outputs may be arrays:


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Local Variables

The names of the input variables given inthe function definition line are local to that

function

i.e., the Function sets up a PRIVATE Workspace

This means that other variable names canbe used when you call the function

All variables inside a function are erased

after the function finishes executing, exceptwhen the same variable names appear in the

output variable list used in the function call.


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Global Variables

Theglobal

command declares certain

variables global, and therefore their values

are available to the basic workspace and to

other functions that declare these variables

global The syntax to declare the variables a, x, and

q as GLOBAL is: global a x q

Any assignment to those variables, in anyfunction or in the base workspace, is

available to all the other functions

declaring them global.


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Private WorkSpace

Cmd Window

WorkSpace

Function-1

WorkSpace

Command

Window

Function

1

INPUTS to

Function-1

OUTPUTS from

Function-1

( 4 3)( 4 3)( 4 3)143


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Make atan2d Functionfunction Q = atan2d(Y,X);

% Bruce Mayer, PE * 8Sep10% ENGR25 * Fcn Lecture%% Modifies Built-in Function

atan2 to return answer in DEGREES%Q = (180/pi)*atan2(Y,X);

>> a1 = atan2d(3,-4)

a1 =

143.1301

>> a2 = atan2d(-3,4)

a2 =

-36.8699

(-4,3)(-4,3)(-4,3)

(4,-3)

37


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All Done for Today

Thisworkspace

for rent


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Bruce Mayer, PELicensed Electrical & Mechanical Engineer

[email protected]

Engr/Math/Physics 25

Appendix 6972 23 xxxxf


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Calling Function drop 1

1. Make as current directory C:\Working_Files_Laptop_0505\BMayer\

Chabot_Engineering\ENGR-25_Comp-

Meth\E25_Demo

2. Use FILE => NEW => M-FILE to open

m-file editor

3. To Slide-28 and Copy the drop Text

4. Paste drop-Text into m-file editor and

save-as drop.m


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Calling Function drop - 2

5. Test drop using SI units>> [y_m, s_mps] = drop(9.8, 2.3, .78)

y_m =

4.7752

s_mps =

9.9440>>


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Calling Function drop - 3

6. The inputs and outputs may be arrays:>> [ft_fall, fps_vel] = drop(32.17,-17, [0:.5:2.5])

ft_fall =0 -4.4787 -0.9150 10.6913 30.3400 58.0313

fps_vel =-17.0000 -0.9150 15.1700 31.2550 47.3400 63.4250

This function call produces the arrays

ft_fall and fps_vel, each with sixvalues corresponding to the six values oftime in the array t.

engr-25 lec-06 sp12 functions-2 builtin udf (1)

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