Introduction to LabVIEW Math Script

Introduction to LabVIEW MathScript

By:Anthony Antonacci

Darryl Morrell

Introduction to LabVIEW MathScript

By:Anthony Antonacci

Darryl Morrell

Online:< http://cnx.org/content/col10370/1.3/ >

C O N N E X I O N S

Rice University, Houston, Texas

This selection and arrangement of content as a collection is copyrighted by Anthony Antonacci. It is licensed under

the Creative Commons Attribution 2.0 license (http://creativecommons.org/licenses/by/2.0/).

Collection structure revised: August 6, 2006

PDF generated: October 30, 2009

For copyright and attribution information for the modules contained in this collection, see p. 51.

Table of Contents

1 LabVIEW MathScript Basics

1.1 Basic operations in LabVIEW MathScript . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Variables in LabVIEW MathScript . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 Vectors and Arrays in LabVIEW MathScript . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.4 Graphical representation of data in LabVIEW MathScript . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2 Programming in LabVIEW MathScript

2.1 A Very Brief Introduction to Programming in LabVIEW MathScript . . . . . . . . . . . . . . . . . . . . . . . 152.2 For Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.3 Conditionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.4 While Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50Attributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

iv

Chapter 1

LabVIEW MathScript Basics

1.1 Basic operations in LabVIEW MathScript1

1.1.1 Basic Operations on Numbers

LABVIEW MATHSCRIPT has many arithmetic operations and functions built in. Most of them arestraightforward to use. The Table (Table 1.1: Common scalar mathematical operations in LABVIEWMATHSCRIPT) below lists some commonly used scalar operations; in this table, x and y are scalars. (Ascalar is a single number.)

Common scalar mathematical operations in LABVIEW MATHSCRIPT

Operation LABVIEW MATHSCRIPT

x− y x-y

x+ y x+y

xy x*y

xy x/y

xy x^y

ex exp(x)

log10 (x) log10(x)

ln (x) log(x)

log2 (x) log2(x)

Table 1.1

Expressions are formed from numbers, variables, and these operations. The operations have di�erentprecedences. The ^ operation has the highest precedence; ^ operations are evaluated before any otheroperations. Multiplication and division have the next highest precedence, and addition and subtraction havethe lowest precedence. Precedence is altered by parentheses; expressions within parenthesesare evaluatedbefore expressions outside parentheses.

Example 1.1The Table (Table 1.2: Example LABVIEW MATHSCRIPT Expressions) below shows severalmathematical formulas, the corresponding LABVIEW MATHSCRIPT expressions, and the valuesthat LABVIEW MATHSCRIPT would compute for the expressions.

1This content is available online at <http://cnx.org/content/m13712/1.1/>.

1

2 CHAPTER 1. LABVIEW MATHSCRIPT BASICS

Example LABVIEW MATHSCRIPT Expressions

3

formula LABVIEW MATHSCRIPTExpression

Computed Value

52 + 42 5^2+4^2 41

(5 + 4)2 (5+4)^2 81

2+34−5 (2 + 3)/(4 - 5) -5

log10 (100) log10(100) 2

ln (4 (2 + 3)) log(4*(2+3)) 2.9957

Table 1.2

1.1.2 Basic Operations on Matrices

In addition to scalars, LABVIEWMATHSCRIPT can operate on matrices. Some common matrix operationsare shown in the Table (Table 1.3: Common matrix mathematical operations in LABVIEW MATHSCRIPT)below; in this table, M and N are matrices.

Common matrix mathematical operations in LABVIEW MATHSCRIPT

Operation LABVIEW MATHSCRIPT

MN M*N

M−1 inv(M)

MT M'

det(M) det(M)

Table 1.3

LABVIEW MATHSCRIPT functions length and size are used to �nd the dimensions of vectors andmatrices, respectively.

LABVIEW MATHSCRIPT can perform an operation on each element of a vector or matrix. To performan arithmetic operation on each element in a vector (or matrix), rather than on the vector (matrix) itself,then the operator should be preceded by ".", e.g .*, .^ and ./.

Example 1.2

Let A =

1 1

1 1

. Then A^2 will return AA =

2 2

2 2

, while A.^2 will return 12 12

12 12

= 1 1

1 1

.Example 1.3Given a vector x, compute a vector y having elements y (n) = 1

sin(x(n)) . This can be easily be done

in LABVIEW MATHSCRIPT by typing y=1./sin(x) Note that using / in place of ./ would resultin the (common) error Matrix dimensions must agree.


1.1.3 Complex numbers

LABVIEW MATHSCRIPT has excellent support for complex numbers with several built-in functions avail-able. The imaginary unit is denoted by i or (as preferred in electrical engineering) j. To create complexvariables z1 = 7 + i and z2 = 2eiπ simply enter z1 = 7 + j and z2 = 2*exp(j*pi)

The Table below gives an overview of the basic functions for manipulating complex numbers, where z isa complex number.

Manipulating complex numbers in LABVIEW MATHSCRIPT

LABVIEW MATHSCRIPT

Re(z) real(z)

Im(z) imag(z)

|z| abs(z)

Angle(z) angle(z)

z∗ conj(z)

Table 1.4

1.1.4 Other Useful Details

• A semicolon added at the end of a line tells LABVIEW MATHSCRIPT to suppress the commandoutput to the display.

• LABVIEWMATHSCRIPT Version 1.0 is case sensitive for both variables and functions; for example,b and B are di�erent variables and LABVIEW MATHSCRIPT will recognize the built-in function sum

but not SUM. In previous versions, LABVIEWMATHSCRIPT was not case sensitive for function names.• Often it is useful to split a statement over multiple lines. To split a statement across multiple lines,

enter three periods ... at the end of the line to indicate it continues on the next line.

Example 1.4Splitting y = a+ b+ c over multiple lines.

y = a...

+ b...

c;

1.2 Variables in LabVIEW MathScript2

1.2.1 Variables in LABVIEW MATHSCRIPT

A variable in LABVIEW MATHSCRIPT is a named value. Using variables allows us to manipulate valuessymbolically, which is particularly useful when programming.

Example 1.5Suppose we wish to compute the circumference of a circle of diameter 5 units using the formulac = πd . We could �rst set the variable d to a value of 5:


5

� d = 5

d =

5.000

Then we could compute the circumference and assign its value to the variable c:

� c = pi*d

c =

15.708

To execute this command, LABVIEW MATHSCRIPT computes the product of the value of d

(which LABVIEW MATHSCRIPT knows because we earlier set it to 5) and the value of pi (whichis a pre de�ned variable in LABVIEW MATHSCRIPT) and stores the value of the product in thevariable c.

Variable names must begin with an upper- or lower-case letter. They may contain letters, digits, andunderscores; they may not contain spaces or punctuation characters. LABVIEW MATHSCRIPT is casesensitive, so A and a are di�erent variables.

Exercise 1.1 (Solution on p. 13.)

Valid variable namesWhich of the following are valid variable names?

1. a2. B3. ecky_ecky_ecky_ecky_ptang_zoo_boing4. ecky ecky ecky ecky ptang zoo boing

5. 2nd6. John-Bigboote

LABVIEW MATHSCRIPT has several prede�ned variables. The most commonly used include

• ans - the default variable in which computation results are stored.• pi - π.• i or j -

√−1 .

Once assigned, variable names remain until they are reassigned or eliminated by the clear command.LABVIEW MATHSCRIPT variables can contain several types of numerical values. These types include

the following:

• Scalar values - scalar is a mathematical term for a single value (i.e. a number). c and d in Example 1.5are scalar variables.

• Vectors - a vector is an ordered series of numbers.• strings - LABVIEW MATHSCRIPT variables may also contain strings of characters.


1.3 Vectors and Arrays in LabVIEW MathScript3

1.3.1 Vectors and Arrays in LABVIEW MATHSCRIPT

An excellent tutorial on how to use LABVIEWMATHSCRIPT's vector and array capabilities is at the InsideLABVIEW MATHSCRIPT Tutorial. 4 Here you can view the general use of LABVIEW MATHSCIRPTand �nd usefull information about data handling capabilities such as arrays and vecotrs.

One useful method of accessing entire rows or entire columns of the matrix is not mentioned in thetutorial. Suppose that the matrix A is de�ned as

�A = [1 2 3 4 5

6 7 8 9 10

11 12 13 14 15

16 17 18 19 20]

A =

1 2 3 4 5

6 7 8 9 10

11 12 13 14 15

16 17 18 19 20

An entire row of A can be obtained by specifying a single ":" as the column index:

�A(2,:)

ans =

6 7 8 9 10

Similarly, an entire column of A can be obtained by specifying a single ":" as the row index:

�A(:,3)

ans =

3

8

13

18

1.4 Graphical representation of data in LabVIEW MathScript5

1.4.1 Graphical representation of data in LABVIEW MATHSCRIPT

LABVIEW MATHSCRIPT provides a great variety of functions and techniques for graphical display of data.The �exibility and ease of use of LABVIEW MATHSCRIPT's plotting tools is one of its key strengths. InLABVIEW MATHSCRIPT graphs are shown in a �gure window. Several �gure windows can be displayedsimultaneously, but only one is active. All graphing commands are applied to the active �gure. The commandfigure(n)will activate �gure number n or create a new �gure indexed by n.

3This content is available online at <http://cnx.org/content/m13727/1.1/>.4http://zone.ni.com/devzone/conceptd.nsf/webmain/76529B03846251A58625709600631C805This content is available online at <http://cnx.org/content/m13728/1.1/>.

7

1.4.2 Tools for plotting

In this section we present some of the most commonly used functions for plotting in LABVIEW MATH-SCRIPT.

• plot- The plot and stem functions can take a large number of arguments, see help plot and help stem.For example the line type and color can easily be changed. plot(y) plots the values in vector yversustheir index. plot(x,y) plots the values in vector yversus x. The plot function produces a piecewiselinear graph between its data values. With enough data points it looks continuous.

• stem- Using stem(y)the data sequence yis plotted as stems from the x-axis terminated with circles forthe data values. stem is the natural way of plotting sequences. stem(x,y) plots the data sequence y

at the values speci�ed in x.• xlabel('string')- Labels the x-axis with string.• ylabel('string')- Labels the y-axis with string.• title('string')- Gives the plot the title string.

To illustrate this consider the following example.

Example 1.6In this example we plot the function y = x2 for x 2 [-2; 2].

x = -2:0.2:2;

y = x.^2;

figure(1);

plot(x,y);

xlabel('x');

ylabel('y=x^2');

title('Simple plot');

figure(2);

stem(x,y);

xlabel('x');

ylabel('y=x^2');

title('Simple stem plot');

This code produces the following two �gures.


Figure 1.1

Figure 1.2

Some more commands that can be helpful when working with plots:

• hold on / o� - Normally hold is o�. This means that the plot command replaces the current plot withthe new one. To add a new plot to an existing graph use hold on. If you want to overwrite the currentplot again, use hold off.

• legend('plot1','plot2',...,'plot N')- The legend command provides an easy way to identifyindividual plots when there are more than one per �gure. A legend box will be added with stringsmatched to the plots.

• axis([xmin xmax ymin ymax])- Use the axis command to set the axis as you wish. Use axis on/off

to toggle the axis on and o� respectively.• subplot(m,n,p) -Divides the �gure window into m rows, n columns and selects the pp'th subplot as the

current plot, e.g subplot(2,1,1) divides the �gure in two and selects the upper part. subplot(2,1,2)selects the lower part.

• grid on/off - This command adds or removes a rectangular grid to your plot.

Example 1.7This example illustrates hold, legend and axis.

x = -3:0.1:3; y1 = -x.^2; y2 = x.^2;

9

figure(1);

plot(x,y1);

hold on;

plot(x,y2,'�');

hold off;

xlabel('x');

ylabel('y_1=-x^2 and y_2=x^2');

legend('y_1=-x^2','y_2=x^2');

figure(2);

plot(x,y1);

hold on;

plot(x,y2,'�');

hold off;

xlabel('x');

ylabel('y_1=-x^2 and y_2=x^2');

legend('y_1=-x^2','y_2=x^2');

axis([-1 1 -10 10]);

The result is shown below.


(a) (b)

Figure 1.3

Example 1.8In this example we illustrate subplot and grid.

x = -3:0.2:3; y1 = -x.^2; y2 = x.^2;

subplot(2,1,1);

plot(x,y1);

xlabel('x'); ylabel('y_1=-x^2');

grid on;

subplot(2,1,2);

plot(x,y2);

xlabel('x');

ylabel('y_2=x^2');

Now, the result is shown below.

11

Figure 1.4

1.4.3 Printing and exporting graphics

After you have created your �gures you may want to print them or export them to graphic �les. In the"File" menu use "Print" to print the �gure or "Save As" to save your �gure to one of the many availablegraphics formats. Using these options should be su�cient in most cases, but there are also a large numberof adjustments available by using "Export setup", "Page Setup" and "Print Setup".

1.4.4 3D Graphics

We end this module on graphics with a sneak peek into 3D plots. The new functions here are meshgrid andmesh. In the example below we see that meshgridproduces xand yvectors suitable for 3D plotting and thatmesh(x,y,z) plots z as a function of both x and y.

Example 1.9Example: Creating our �rst 3D plot.

[x,y] = meshgrid(-3:.1:3);

z = x.^2+y.^2;

mesh(x,y,z);

xlabel('x');

ylabel('y');

zlabel('z=x^2+y^2');

This code gives us the following 3D plot.


Figure 1.5

13

Solutions to Exercises in Chapter 1

Solution to Exercise 1.1 (p. 5)

1. Valid.2. Valid.3. Valid.4. Invalid, because the variable name contains spaces.5. Invalid, because the variable name begins with a number.6. Invalid, because the variable name contains a dash.


Chapter 2

Programming in LabVIEW MathScript

2.1 A Very Brief Introduction to Programming in LabVIEW

MathScript1

You can use LABVIEWMathScript code to automate computations. Almost anything typed at the commandline can also be included in a LABVIEW MathScript program. Lines in a LABVIEW MathScript script areinterpreted sequentially and the instructions are executed in turn. This simpli�es repetitive computations.This allows you to create complex computations that cannot be readily implemented using commands at thecommand line. You can also create computational capabilities for other people to use.

LABVIEW MATHSCRIPT scripts are text �les and can be edited by any text editor. Any script shouldrun the same on any computer running LABVIEW MATHSCRIPT regardless of its operating system. Script�les must have an extension of ".m" and be in a directory that LABVIEW MATHSCRIPT knows about.

LABVIEW MATHSCRIPT scripts interact with the current LABVIEW MathScript environment. Vari-ables set before the script is executed can a�ect what happens in the script. Variables set in the scriptremain after the script has �nished execution.

One way to edit LABVIEW MATHSCRIPT scripts is to use the built-in editor. The editor has some fea-tures that make editing LABVIEWMATHSCRIPT scripts easier. The editor is integrated with the debuggerwhich makes �nding and correcting errors in your scripts easier. More detailed information about editingscripts can be found at National Instruments LabVIEW MathScript Tutorial-Inside LabVIEW MathScriptTutorial2 .

Use comments to remind you and help other users understand how you have implemented your program.Comments begin with the character %.

For LABVIEW MATHSCRIPT to correctly execute a script, it must know the directory in which thescript resides. There are several ways to do this. One is to set the current working directory for LABVIEWMATHSCRIPT from the File>MathScript Preferences in the MathScript interactive window. More detailedinformation can be found at National Instrument's LabVIEW MathScript Preferences Dialog Box3 .

M-�le names should begin with a letter and only contain letters and numbers. Any other characters(space, dash, star, slash, etc.) will be interpreted by LABVIEW MATHSCRIPT as operations on variablesand will cause errors. Also, M-�le names should not be the same as variables in the workspace, sinceLABVIEW MATHSCRIPT will not be able to di�erentiate between the �le name and the variable.

1This content is available online at <http://cnx.org/content/m13713/1.1/>.2http://zone.ni.com/devzone/conceptd.nsf/webmain/76529B03846251A58625709600631C803http://zone.ni.com/reference/en-XX/help/371361A-01/lvdialog/mathscript_preferences_db/

15

16 CHAPTER 2. PROGRAMMING IN LABVIEW MATHSCRIPT

2.2 For Loops

2.2.1 Programming in LabVIEW MathScript-For Loops4

2.2.1.1 The For Loop

The for loop is one way to make LABVIEW MATHSCRIPT repeat a series of computations using di�erentvalues. The for loop has the following syntax:

for d = array

% LABVIEW MATHSCRIPT command 1


% and so on

end

In the for loop, array can be any vector or array of values. The for loop works like this: d is set to the �rstvalue in array, and the sequence of LABVIEW MATHSCRIPT commands in the body of the for loop isexecuted with this value of d. Then d is set to the second value in array, and the sequence of LABVIEWMATHSCRIPT commands in the body of the for loop is executed with this value of d. This process continuesthrough all of the values in array. So a for loop that performs computations for values of d from 1.0 to 2.0is:

for d = 1.0:0.05:2.0



% and so on

end

(Recall that 1.0:0.05:2.0 creates a vector of values from 1.0 to 2.0.)Note that in all of the examples in this module, the LABVIEW MATHSCRIPT commands inside the for

loop are indented relative to the for and end statements. This is not required by LABVIEW MATHSCRIPTbut is common practice and makes the code much more readable.

A useful type of for loop is one that steps a counter variable from 1 to some upper value:

for j = 1:10

% LABVIEW MATHSCRIPT commands

end

For example, this type of loop can be used to compute a sequence of values that are stored in the elementsof a vector. An example of this type of loop is

% Store the results of this loop computation in the vector v

for j = 1:10

% LABVIEW MATHSCRIPT commands

% More LABVIEW MATHSCRIPT commands to compute a complicated result

v(j) = result;

end

Using a for loop to access and manipulate elements of a vector (as in this example) may be the mostnatural approach, particularly when one has previous experience with other programming languages such as


17

C or Java. However, many problems can be solved without for loops by using LABVIEW MATHSCRIPT'sbuilt-in vector capabilities. Using these capabilities almost always improves computational speed and reducesthe size of the program. Some would also claim that it is more elegant.

For loops can also contain other for loops. For example, the following code performs the LABVIEWMATHSCRIPT commands for each combination of d and c:

for d=1:0.05:2

for c=5:0.1:6

% LABVIEW MATHSCRIPT Commands

end

end

2.2.2 Programming in LabVIEW MathScript-Simple For Loop Exercises5

2.2.2.1 Some For Loop Exercises


Loop IndicesHow many times will this program print "Hello World"?

for a=0:50

disp('Hello World')

end


Loop Indices IIHow many times will this program print "Guten Tag Welt"?

for a=-1:-1:-50

disp('Guten Tag Welt')

end


Loop Indices IIIHow many times will this program print "Bonjour Monde"?

for a=-1:1:-50

disp('Bonjour Monde')

end


Nested LoopsHow many times will this program print "Hola Mundo"?

for a=10:10:50

for b=0:0.1:1

disp('Hola Mundo')

end

end




A tricky loopWhat sequence of numbers will the following for loop print?

n = 10;

for j = 1:n

n = n-1;

j

end

Explain why this code does what it does.


Nested Loops IIWhat value will the following program print?

count = 0;

for d = 1:7

for h = 1:24

for m = 1:60

for s = 1:60

count = count + 1;

end

end

end

end

count

What is a simpler way to achieve the same results?


Multiple Hypotenuses

ac

b

Figure 2.1: Sides of a right triangle.

Consider the right triangle shown in Figure 2.1. Suppose you wish to �nd the length of the hy-potenuse c of this triangle for several combinations of side lengths a and b; the speci�c combinationsof a and b are given in Table 2.1: Side Lengths. Write a LABVIEW MATHSCRIPT's program todo this.

19

Side Lengths

a b

1 1

1 2

2 3

4 1

2 2

Table 2.1

2.2.3 Programming in LabVIEW MathScript-A Modeling Example Using For

Loops6

2.2.3.1 A Modeling Problem: Counting Ping Pong Balls

Suppose you have a cylinder of height h with base diameter b (perhaps an empty pretzel jar), and you wishto know how many ping-pong balls of diameter d have been placed inside the cylinder. How could youdetermine this?

note: This problem, along with the strategy for computing the lower bound on the number ofping-pong balls, is adapted from (Star�eld 1994). [1]

A lower bound for this problem is found as follows:

• NL -Lower bound on the number of balls that �t into the cylinder.• Vcyl -The volume of the cylinder.

Vcyl = hπ

(b

2

)2

(2.1)

• Vcube -The volume of a cube that encloses a single ball.

Vcube = d3 (2.2)

The lower bound is found by dividing the volume of the cylinder by the volume of the cube enclosing a singleball.

NL =VcylVcube

(2.3)


The interactive approachYou are given the following values:

• d = 1.54in• b = 8in• h = 14in



Use LABVIEWMATHSCRIPT interactively (that is, type commands at the command line prompt)to compute NL .


Using an M-FileCreate an M-File to solve Problem 2.8 (The interactive approach).

To complicate your problem, suppose that you have not been given values for d, b, and h. Instead youare required to estimate the number of ping pong balls for many di�erent possible combinations of thesevariables (perhaps 50 or more combinations). How can you automate this computation?

In LABVIEW MATHSCRIPT, one way to automate the computation of NL for many di�erent combi-nations of parameter values is to use a for loop. (Read Programming in LABVIEW MATHSCRIPT-ForLoops (Section 2.2.1) if you are not familiar with the use of for loops in LABVIEW MATHSCRIPT.) Thefollowing problems ask you to develop several di�erent ways that for loops can be used to automate thesecomputations.


Use a for loopAdd a for loop to your M-File from Problem 2.9 (Using an M-File) to compute NL for b = 8in,h = 14in, and values of d ranging from 1.0 in to 2.0 in.


Can you still use a for loop?Modify your M-File from Problem 2.10 (Use a for loop) to plot NL as a function of d for b = 8inand h = 14in.Exercise 2.12 (Solution on p. 37.)

More loops?Modify your M-File from Problem 2.10 (Use a for loop) to compute NL for d = 1.54in and variousvalues of b and h.

2.2.4 Programming in LabVIEW MathScript-A Data Analysis Example Using

For Loops7

note: This example requires an understanding of the relationships between position, velocity,and acceleration of an object moving in a straight line. The Wikipedia article Motion Graphs andDerivatives8 has a clear explanation of these relationships, as well as a discussion of average andinstantaneous velocity and acceleration and the role derivatives play in these relationships. Also,in this example, we will approximate derivatives with forward, backward, and central di�erences;Lecture 4.1 by Dr. Dmitry Pelinovsky at McMaster University 9 contains useful information aboutthis approximation. We will also approximate integrals using the trapezoidal rule; The Wikipediaarticle Trapezium rule10 has an explanation of the trapezoidal rule.

2.2.4.1 Trajectory Analysis of an Experimental Homebuilt Rocket

On his web page Richard Nakka's Experimental Rocketry Web Site: Launch Report - Frost�re Two Rocket11

, Richard Nakka provides a very detailed narrative of the test �ring of his Frost�re Two homebuilt rocket andsubsequent data analysis. (His site12 provides many detailed accounts of tests of rockets and rocket motors.

7This content is available online at <http://cnx.org/content/m13715/1.1/>.8http://en.wikipedia.org/wiki/Motion_graphs_and_derivatives9http://dmpeli.math.mcmaster.ca/LabVIEW MathScript/Math1J03/LectureNotes/Lecture4_1.htm

10http://en.wikipedia.org/wiki/Trapezoidal_rule11http://www.nakka-rocketry.net/�-2.html12http://www.nakka-rocketry.net/

21

Some rocket launches were not as successful as the Frost�re Two launch; his site provides very interestingpost-�ight analysis of all launches.)

2.2.4.2 Computation of Velocity and Acceleration from Altitude Data

In this section, we will use LABVIEW MATHSCRIPT to analyze the altitude data extracted from theplot "Altitude and Acceleration Data from R-DAS" on Richard Nakk's web page. This data is in the �leAltitude.csv13 . We will use this data to estimate velocity and acceleration of the Frost�re Two rocket duringits �ight.

Exercise 2.13Get the dataDownload the altitude data set in the �le Altitude.csv14 (right click on the �le's link) onto yourcomputer. Then be sure to save the �le to your MATHSCRIPT working directory. This can bedetermined by navigating to the File/MathScript Perferences tab. The �le is formatted as twocolumns: the �rst column is time in seconds, and the second column is altitude in feet. Load thedata into LABVIEW MATHSCRIPT and plot the altitude as a function of time.

The following sequence of LABVIEW MATHSCRIPT commands will load the data, create a vector t oftime values, create a vector s of altitude values, and plot the altitude as a function of time.

Altitude = csvread('Altitude.csv');

t =Altitude(:,1);

s =Altitude(:,2);

plot(t,s)

The plot should be similar to that in Figure 2.2.

0 50 100 1500

1000

2000

3000

4000

5000

6000

Figure 2.2: Plot of altitude versus time.

13http://cnx.org/content/m13715/latest/Altitude.csv14http://cnx.org/content/m13715/latest/Altitude.csv



Forward Di�erencesWrite a LABVIEW MATHSCRIPT script that uses a for loop to compute velocity and accelerationfrom the altitude data using forward di�erences. Your script should also plot the computed velocityand acceleration as function of time.


Backward Di�erencesModify your script from Problem 2.14 (Forward Di�erences) to compute velocity and accelerationusing backward di�erences. Remember to save your modi�ed script with a di�erent name thanyour script from Problem 2.14 (Forward Di�erences).


Central Di�erencesModify your script from Problem 2.14 (Forward Di�erences) to compute velocity and accelerationusing central di�erences. Remember to save your modi�ed script with a di�erent name than yourscript from Problem 2.14 (Forward Di�erences) and Problem 2.15 (Backward Di�erences).

Compare the velocity and acceleration values computed by the di�erent approximations. What can you sayabout their accuracy?


Can it be done without loops?Modify your script from Problem 2.14 (Forward Di�erences) to compute velocity and accelerationwithout using a for loop.

2.2.4.3 Computation of Velocity and Altitude from Acceleration Data

In this section, we will use LABVIEW MATHSCRIPT to analyze the acceleration data extracted from theplot "Altitude and Acceleration Data from R-DAS" on Richard Nakk's web page. Download the accelerationdata set in the �le Acceleration.csv15 (right click on the �le's link) onto your computer. The �rst column istime in seconds, and the second column is acceleration in g's. The following commands load the data intoLABVIEW MATHSCRIPT and plot the acceleration as a function of time.

Acceleration = csvread('Acceleration.csv');

t = Acceleration(:,1);

a = Acceleration(:,2);

plot(t,a)

The plot should be similar to that in Figure 2.3.

15http://cnx.org/content/m13715/latest/Acceleration.csv

23

0 50 100 150−10

−5

0

5

10

Figure 2.3: Plot of acceleration versus time.


Trapezoidal RuleWrite a LABVIEW MATHSCRIPT script that uses a for loop to compute velocity and altitudefrom the acceleration data using the trapezoidal rule. Your script should also plot the computedvelocity and altitude as function of time.


Can it be done without loops?Modify your script from Problem 2.18 (Trapezoidal Rule) to compute velocity and altitude withoutusing a for loop.

2.3 Conditionals

2.3.1 Programming in LabVIEW MathScript-If Statements16

2.3.1.1 The If Statement

The if statement is one way to make the sequence of computations executed by LABVIEW MATHSCRIPTdepend on variable values. The if statement has several di�erent forms. The simplest form is

if expression

% LABVIEW MATHSCRIPT commands to execute if expression is true

end

where expression is a logical expression that is either true or false. (Information about logical expressions isavailable in Programming in LABVIEW MATHSCRIPT-Logical Expressions (Section 2.3.2).) For example,the following if statement will print "v is negative" if the variable v is in fact negative:



if v < 0

disp('v is negative')

end

A more complicated form of the if statement is

if expression

% LABVIEW MATHSCRIPT commands to execute if expression is true

else

% LABVIEW MATHSCRIPT commands to execute if expression is false

end

For example, the following if statement will print "v is negative" if the variable v is negative and "v is notnegative" if v is not negative:

if v < 0


else

disp('v is not negative')

end

The most general form of the if statement is

if expression1

% LABVIEW MATHSCRIPT commands to execute if expression1 is true

elseif expression2


elseif expression3


...

else

% LABVIEW MATHSCRIPT commands to execute if all expressions are false

end

The following if statement is an example of this most general statement:

if v < 0


elseif v > 0

disp('v is positive')

else

disp('v is zero')

end

Note that in all of the examples in this module, the LABVIEW MATHSCRIPT commands inside theif statement are indented relative to the if, else, elseif, and end statements. This is not required byLABVIEW MATHSCRIPT but is common practice and makes the code much more readable.

25

2.3.2 Programming in LabVIEW MathScript-Logical Expressions17

2.3.2.1 Logical Expressions

Logical expressions are used in if statements (Section 2.3.1), switch case statements, and while loops (Sec-tion 2.4.1) to change the sequence of execution of LABVIEW MATHSCRIPT commands in response tovariable values. A logical expression is one that evaluates to either true or false. For example, v > 0 is alogical expression that will be true if the variable v is greater than zero and false otherwise.

note: In LABVIEW MATHSCRIPT, logical values (true and false) are actually represented bynumerical values. The numerical value of zero represents false, and any nonzero numerical valuerepresents true.

Logical expression are typically formed using the following relational operators:

Relational Operators

Symbol Relation

< Less than

<= Less than or equal to

> Greater than

>= Greater than or equal to

== Equal to

∼= Not equal to

Table 2.2

note: == is not the same as =; LABVIEW MATHSCRIPT's treats them very di�erently. ==

compares two values, while = assigns a value to a variable.

Complex logical expressions can be created by combining simpler logical expressions using the followinglogical operators:

Logical Operators

Symbol Relation

∼ Not

&& And

|| Or

Table 2.3

2.3.3 Programming in LabVIEW MathScript-Simple If Statement Exercises18

2.3.3.1 Some If Statement Exercises


What will the following LABVIEW MATHSCRIPT code print?

17This content is available online at <http://cnx.org/content/m13721/1.2/>.18This content is available online at <http://cnx.org/content/m13724/1.1/>.


a = 10;

if a ∼= 0

disp('a is not equal to 0')

end



a = 10;

if a > 0

disp('a is positive')

else

disp('a is not positive')

end



a = 5;

b = 3;

c = 2;

if a < b*c

disp('Hello world')

else

disp('Goodbye world')

end


Suppose the code in Problem 2.21 is modi�ed by adding parentheses around a > 0. What will itprint?

a = 10;

if (a > 0)

disp('a is positive')

else

disp('a is not positive')

end


Suppose the code in Problem 2.22 is modi�ed by adding the parentheses shown below. What willit print?

a = 5;

b = 3;

c = 2;

if (a < b)*c

disp('Hello world')

else


end

27



p1 = 3.14;

p2 = 3.14159;

if p1 == p2

disp('p1 and p2 are equal')

else

disp('p1 and p2 are not equal')

end



a = 5;

b = 10;

if a = b

disp('a and b are equal')

else

disp('a and b are not equal')

end


For what values of the variable a will the following LABVIEW MATHSCRIPT code print 'Helloworld'?

if ∼ a == 0

disp('Hello world')

else


end



if a >= 0 && a < 7

disp('Hello world')

else


end



if a < 3 || a > 10

disp('Hello world')

else


end




if a < 7 || a >= 3

disp('Hello world')

else


end


Write an if statement that will print 'a is very close to zero' if the value of the variable ais between -0.01 and 0.01.

2.3.4 Programming in LabVIEW MathScript-An Engineering Cost Analysis Ex-

ample Using If Statements19

2.3.4.1 An Engineering Cost Analysis Example

Suppose you are a design engineer for a company that manufactures consumer electronic devices and youare estimating the cost of producing a new product. The product has four components that are purchasedfrom electronic parts suppliers and assembled in your factory. You have received cost information from yoursuppliers for each of the parts; as is typical in the electronics industry, the cost of a part depends on thenumber of parts you order from the supplier.

Your assembly cost for each unit include the cost of labor and your assembly plant. You have estimatedthat these costs are C0=$45.00/unit.

The cost of each part depends on the number of parts purchased; we will use the variable n to representthe number of parts, and the variables CA, CB, CC, and CD to represent the unit cost of each type of part.These cost are given in the following tables.

Unit cost of Part A

n CA

1-4 $16.00

5-24 $14.00

25-99 $12.70

100 or more $11.00

Table 2.4

Unit cost of Part B

n CB

continued on next page


29

1-9 $24.64

10-49 $24.32

50-99 $24.07

100 or more $23.33

Table 2.5

Unit cost of Part C

n CC

1-24 $17.98

25-49 $16.78

50 or more $15.78

Table 2.6

Unit cost of Part D

n CD

1-9 $12.50

10-99 $10.42

100 or more $9.62

Table 2.7

The unit cost is Cunit = C0 + CA + CB + CC + CD. To �nd the unit cost to build one unit, we look inthe above tables with a value of n=1; the unit cost is

$45.00+$16.00+$24.64+$17.98+$12.50 = $116.12

To �nd the unit cost to build 20 units, we look in the above tables with a value of n=20 and get

$45.00+$14.00+$24.32+$17.98+$10.42 = $109.72

As expected, the unit cost for 20 units is lower than the unit cost for one unit.


Create an if statement that will assign the proper cost to the variable CA based on the value ofthe variable n.


Create a LABVIEW MATHSCRIPT program that will compute the total unit cost Cunit for agiven value of the variable n.


Create a LABVIEW MATHSCRIPT program that will compute and plot the total unit cost as afunction of n for values of n from 1 to 150.


2.4 While Loops

2.4.1 Programming in LabVIEW MathScript-While Loops20

2.4.1.1 The While Loop

The while loop is similar to the for loop in that it allows the repeated execution of LABVIEW MATH-SCRIPT statements. Unlike the for loop, the number of times that the LABVIEW MATHSCRIPT state-ments in the body of the loop are executed can depend on variable values that are computed in the loop.The syntax of the while loop has the following form:

while expression



% More commands to execute repeatedly until expression is not true

end

where expression is a logical expression that is either true or false. (Information about logical expressions isavailable in Programming in LABVIEW MATHSCRIPT-Logical Expressions (Section 2.3.2).) For example,consider the following while loop:

n = 1

while n < 3

n = n+1

end

This code creates the following output:

n =

1

n =

2

n =

3

Note that in all of this example, the LABVIEW MATHSCRIPT commands inside the while loop areindented relative to the while and end statements. This is not required by LABVIEW MATHSCRIPT butis common practice and makes the code much more readable.

2.4.2 Programming in LabVIEW MathScript-Simple While Loop Exercises21

2.4.2.1 Some While Loop Exercises


How many times will this loop print 'Hello World'?

20This content is available online at <http://cnx.org/content/m13722/1.2/>.21This content is available online at <http://cnx.org/content/m13725/1.1/>.

31

n = 10;

while n > 0

disp('Hello World')

n = n - 1;

end


How many times will this loop print 'Hello World'?

n = 1;

while n > 0

disp('Hello World')

n = n + 1;

end


What values will the following LABVIEW MATHSCRIPT code print?

a = 1

while a < 100

a = a*2

end


What values will the following LABVIEW MATHSCRIPT code print?

a = 1;

n = 1;

while a < 100

a = a*n

n = n + 1;

end

2.4.3 Programming in LabVIEWMathScript-A Personal Finance Example Using

While Loops22

2.4.3.1 A Personal Finance Example

A student decides to �nance their college education using a credit card. They charge one semester's tuitionand then make the minimum monthly payment until the credit card balance is zero. How many months willit take to pay o� the semester's tuition? How much will the student have spent to pay o� the tuition?

We can solve this problem using LABVIEW MATHSCRIPT. We de�ne the following variables:

• bn - Balance at month n.• pn - Payment in month n.• fn - Finance charge (interest) in month n.



The �nance charge fnis the interest that is paid on the balance each month. The �nance charge iscomputed using the monthly interest rate r:

fn = rbn (2.4)

Credit card interest rates are typically given as an annual percentage rate (APR). To convert the APR toa monthly interest rate, use the following formula:

r =(

1 +APR100

) 112

− 1 (2.5)

More information on how to compute monthly rates can be found here23 .Credit cards usually have a minimum monthly payment. The minimum monthly payment is usually

a �xed percentage of the balance; the percentage is required by federal regulations to be at least 1% higherthan the monthly interest rate. If this minimum payment would be below a given threshold (usually $10 to$20), the minimum payment is instead set to the threshold. For a threshold of $10, the relationship betweenthe balance and the minimum payment can be shown in an equation as follows:

pn = max ((r + 0.01) bn, 10) (2.6)

To compute the balance for one month (month n+ 1) from the balance for the previous month (monthn), we compute the �nance charge on the balance in the previous month and add it to the previous balance,then subtract the payment for the previous month:

bn+1 = bn + fn − pn (2.7)

In the following exercises, we will develop the LABVIEW MATHSCRIPT program to compute thenumber of months necessary to pay the debt. We will assume that the card APR is 14.9% (the average rateon a student credit card24 in mid February 2006) and that the initial balance charged to the card is $2203(the in-state tuition at the Polytechnic Campus of Arizona State University for Spring 2006 semester25 ).


Write LABVIEW MATHSCRIPT code to compute the monthly interest rate r from the APRusing (2.5).


Write LABVIEW MATHSCRIPT code to compute the minimum monthly payment pn using (2.6).


Write LABVIEW MATHSCRIPT code to compute the balance at month n + 1 in terms of thebalance at month n using (2.7).


Place the code developed for Exercise 2.41 into a while loop to determine how many months willbe required to pay o� the card.


Modify your code from Exercise 2.42 to plot the monthly balance, monthly payment, and totalcost-to-date for each month until the card is paid o�.

23http://en.wikipedia.org/wiki/Credit_card_interest24http://money.cnn.com/pf/informa/index.html25http://www.asu.edu/sbs/FallUndergradEastWest.htm

33

Solutions to Exercises in Chapter 2

Solution to Exercise 2.1 (p. 17)The code 0:50 creates a vector of integers starting at 0 and going to 50; this vector has 51 elements. "HelloWorld" will be printed once for each element in the vector (51 times).Solution to Exercise 2.2 (p. 17)The code -1:-1:-50 creates a vector of integers starting at -1 and going backward to -50; this vector has50 elements. "Guten Tag Welt" will be printed once for each element in the vector (50 times).Solution to Exercise 2.3 (p. 17)The code -1:1:-50 creates an empty vector with no elements. Since this is an empty vector the followingerror occurs: "Error in function range at line 1. You cannot specify a step size of zero for a range."Solution to Exercise 2.4 (p. 17)The outer loop (the loop with a) will be executed �ve times. Each time the outer loop is executed, theinner loop (the loop with b) will be executed eleven times, since 0:0.1:1 creates a vector with 11 elements."Hola Mundo" will be printed 55 times.Solution to Exercise 2.5 (p. 18)In the �rst line, the value of n is set to 10. The code 1:n creates a vector of integers from 1 to 10. Eachiteration through the loop sets j to the next element of this vector, so j will be sent to each value 1 through10 in succession, and this sequence of values will be printed. Note that each time through the loop, the valueof n is decreased by 1; the �nal value of n will be 0. Even though the value of n is changed in the loop, thenumber of iterations through the loop is not a�ected, because the vector of integers is computed once beforethe loop is executed and does not depend on subsequent values of n.Solution to Exercise 2.6 (p. 18)The d loop will be executed seven times. In each iteration of the d loop, the h loop will be executed 24times. In each iteration of the h loop, the m loop will be executed 60 times. In each iteration of the m loop,the s loop will be executed 60 times. So the variable count will be incremented 7× 24× 60× 60 = 604800times.

A simpler way to achieve the same results is the command

7*24*60*60

Solution to Exercise 2.7 (p. 18)This solution was created by Heidi Zipperian:

a=[1 1 2 4 2]

b=[1 2 3 1 2]

for j=1:5

c=sqrt(a(j)^2+b(j)^2)

end

A solution that does not use a for loop was also created by Heidi:

a=[1 1 2 4 2]

b=[1 2 3 1 2]

c=sqrt(a.^2+b.^2)

Solution to Exercise 2.8 (p. 19)The following shows commands typed to LABVIEW MATHSCRIPT (at the � command window) and theoutput produced by LABVIEW MATHSCRIPT:


�d = 1.54

d =

1.54

�b = 8

b =

8

�h = 14

h =

14

�vcyl = h*pi*(b/2)^2

vcyl =

703.72

�vcube = d^3

vcube =

3.6523

�nl = vcyl/vcube

nl =

192.68

Solution to Exercise 2.9 (p. 20)We used the LABVIEW MATHSCRIPT editor (or any text editor) to create the following �le namedPingPong.m:

% PingPong.m - computes a lower bound on the number of

% ping pong balls that fit into a cylinder

% Note that most lines end with a ";", so they don't print

% intermediate results

d = 1.54;

h = 14;

b = 8;

vcyl = h*pi*(b/2)^2;

vcube = d^3;

nl = vcyl/vcube

When run from the LABVIEW MATHSCRIPT command line, this program produces the following output:

35

� PingPong

nl =

192.6796

Solution to Exercise 2.10 (p. 20)This solution is by BrieAnne Davis.

for d=1.0:.05:2.0

b=8;

h=14;

vcyl=h*pi*(b/2)^2

vcube=d^3

nl=vcyl/vcube

end

Solution to Exercise 2.11 (p. 20)This solution is by Wade Stevens. Note that it uses the LABVIEW MATHSCRIPT hold on commandafter the plot statement to plot each point individually in the for loop.

clear all

for d=1.0:0.1:2.0;

b=8;

h=14;

C=h*pi*(b/2)^2; %volume of cylinder

c=d^3; %volume of cube

N=C/c; %Lower bound

floor(N)

plot (d,N,'g*')

hold on

end

This solution creates the plot in Figure 2.4.


1 1.2 1.4 1.6 1.8 20

100

200

300

400

500

600

700

800

Figure 2.4: Plot of NL as a function of d; each point plotted individually.

This di�erent solution is by Christopher Embrey. It uses the index variable j to step through the dv

array to compute elements of the nlv array; the complete nlv array is computed, and then plotted outsidethe for loop.

clear

dv=1.0:.05:2.0;

[junk,dvsize] = size(dv)

for j=1:dvsize

d=dv(j)

b=8; %in

h=14; %in

vcyl=h*pi*(b/2)^2;

vcube=d^3;

nl=vcyl/vcube;

nlv(j)=nl;

end

plot (dv,nlv)

This solution creates the plot in Figure 2.5.

37

1 1.2 1.4 1.6 1.8 20

100

200

300

400

500

600

700

800

Figure 2.5: Plot of NL as a function of d; points plotted as vectors.

And �nally, this solution by Travis Venson uses LABVIEW MATHSCRIPT's vector capabilities to per-form the computation without a for loop.

%creates a vector for diameter

dv=1:.02:2;

b=5.5;

h=12;

%computes volume of cylinder

vcyl=h*pi*(b/2)^2;

%computes volume of cube

vcube=dv.^3;

%computes lower bound

lowerboundv=vcyl./vcube;

%plots results

plot(dv,lowerboundv)

Solution to Exercise 2.12 (p. 20)This solution is by AJ Smith. The height, h, ranges from 12 to 15 and the base, b, ranges from 8 to 12.

for h=12:15; %ranges of height

for b=8:12; %ranges of the base

d=1.54; %diameter of ping pong ball.

Vcyl=h*pi*(b/2)^2; %Volume of cylinder

Vcube=d^3; %volume of a cube that encloses a single ball

Nl=Vcyl/Vcube %lower bound on the number of balls that fit in the cylinder


end

end

Solution to Exercise 2.14 (p. 21)This solution is by Scott Jenne; it computes and plots the velocity:


t=Altitude(:,1);

s=Altitude(:,2);

for n=1:180;

v=((s(n+1))-s(n))/((t(n+1))-t(n));

hold on

plot(t(n),v,'o')

end

The plot produced by this code is shown in Figure 2.6.

0 50 100 150−200

0

200

400

600

800

Figure 2.6: Plot of velocity computed with the forward di�erence method versus time.

Solution to Exercise 2.15 (p. 22)This solution by Bryson Hinton:


t=Altitude(:,1);

s=Altitude(:,2);

for x=2:181

v(x)=(s(x)-s(x-1))/(t(x)-t(x-1));

plot(t(x),v(x),'b.')

hold on

end


39

0 50 100 150−200

0

200

400

600

800

Figure 2.7: Plot of velocity computed with the backward di�erence method versus time.

Solution to Exercise 2.16 (p. 22)This code computes the velocity using the central di�erence formula.

clear all


t=Altitude(:,1);

s=Altitude(:,2);

for n=2:180

v(n-1)=(s(n+1)-s(n-1))/(t(n+1)-t(n-1));

end

plot(t(2:180),v)


Figure 2.8: Plot of velocity computed with the central di�erence method versus time.

Solution to Exercise 2.17 (p. 22)This code uses LABVIEW MATHSCRIPT's diff function to compute the di�erence between adjacient ele-ments of t and s, and the ./ function to divide each element of the altitude di�erences with the correspondingelement of the time di�erences:

clear all


t=Altitude(:,1);

s=Altitude(:,2);

v=diff(s)./diff(t);

plot(t(1:180),v)



0 50 100 150−200

0

200

400

600

800

Figure 2.9: Plot of velocity computed with the forward di�erence method versus time. The values inthis plot are the same as in Figure 2.6.

Solution to Exercise 2.18 (p. 23)This solution is by Jonathan Selby:


t=Acceleration (:,1);

a=Acceleration (:,2);

v(1)=0;

for n=1:181

v(n+1)=(t(n+1)-t(n))*(a(n+1)+a(n))/2+v(n);

end

plot(t,v)

This code creates the plot in Figure 2.10.

41

0 50 100 150−100

−80

−60

−40

−20

0

20

40

Figure 2.10: Plot of velocity versus time. The velocity is computed by numerically integrating themeasured acceleration.

This code can be easily extended to also compute altitude while it is computing velocity:


t=Acceleration (:,1);

a=Acceleration (:,2);

v(1)=0; % Initial velocity

s(1)=0; % Initial altitude

for n=1:181

v(n+1)=(t(n+1)-t(n))*(a(n+1)+a(n))/2+v(n);

s(n+1)=(t(n+1)-t(n))*(v(n+1)+v(n))/2+s(n);

end

plot(t,s)

This code creates the plot in Figure 2.11.


0 50 100 150−5000

−4000

−3000

−2000

−1000

0

1000

Figure 2.11: Plot of altitude versus time.

Solution to Exercise 2.19 (p. 23)This solution by Nicholas Gruman uses the LABVIEW MATHSCRIPT trapz function to compute velocitywith the trapezoidal rule with respect to time at all given points in time:


t=Acceleration(:,1);

A=Acceleration(:,2);

c = length(t);

for i = 1:c

v(i)=trapz(t(1:i),A(1:i));

end

Altitude could also be computed by adding the following line in the same For loop as the previous code:

s(i)=trapz(t(1:i),v(1:i));

Solution to Exercise 2.20 (p. 25)' a is not equal to 0'Solution to Exercise 2.21 (p. 26)' a is positive'Solution to Exercise 2.22 (p. 26)b*c gives a value of 6, and 5 < 6, so this code will print 'Hello world'.

Solution to Exercise 2.23 (p. 26)The parentheses around the relational expression a > 0 will not change its validity, so this code will print'a is positive'.Solution to Exercise 2.24 (p. 26)The parentheses in this expression change its meaning completely. First, a < b is evaluated, and since itis false for the given values of a and b, it evaluates to zero. The zero is than multiplied by c, giving a valueof zero which is interpreted by LABVIEW MATHSCRIPT as false. So this code prints 'Goodbye world'.Solution to Exercise 2.25 (p. 27)' p1 and p2 are not equal'

43

Solution to Exercise 2.26 (p. 27)This code will generate an error message, since a = b assigns the value of b to a. To check if a and b areequal, use a == b.Solution to Exercise 2.27 (p. 27)Any value that is not zero.Solution to Exercise 2.28 (p. 27)Any value greater than or equal to 0 and less than 7.Solution to Exercise 2.29 (p. 27)Any value less than 3 or greater than 10.Solution to Exercise 2.30 (p. 28)Every value of a will print 'Hello world'.Solution to Exercise 2.31 (p. 28)

if a >= -0.01 && a <= 0.01

disp('a is very close to zero')

end


if n >= 1 && n <= 4

CA = 16.00;

elseif n >= 5 && n <= 24

CA = 14.00;

elseif n >= 25 && n <= 99

CA = 12.70;

else

CA = 11.00;

end

Solution to Exercise 2.33 (p. 29)This code by BrieAnne Davis:

if n>=1 && n<=4;%if n=1 to 4, CA is $16.00

CA=16.00;

elseif n>=5 && n<=24;%if n=5 to 24, CA is $14.00

CA=14.00;

elseif n>=25 && n<=99;%if n=25 to 99, CA is $12.70

CA=12.70;

elseif n>=100;%if n=100 or more, CA is $11.00

CA=11.00;

end%this ends the if statement for CA

if n>=1 && n<=9;%if n=1 to 9, CB is $24.64

CB=24.64;

elseif n>=10 && n<=49;%if n=10 to 49, CB is $24.32

CB=24.32;

elseif n>=50 && n<=99;%if n=50 to 99, CB is $24.07

CB=24.07;


elseif n>=100;%if n=100 or more, CB is $23.33

CB=23.33;

end%this ends the if statement for CB

if n>=1 && n<=24;%if n=1 to 24, CC is $17.98

CC=17.98;

elseif n>=25 && n<=49;%if n=25 to 49, CC is $16.78

CC=16.78;

elseif n>=50;%if n=50 or more, CC is $15.78

CC=15.78;

end%this ends the if statement for CC

if n>=1 && n<=9;%if n=1 to 9, CD is $12.50

CD=12.50;

elseif n>=10 && n<=99;%if n=10 to 99, CD is $10.42

CD=10.42;

elseif n>=100;%if n=100 or more, CD is $9.62

CD=9.62;

end%this ends the if statement

CO=45.00;

Cunit=CO + CA + CB + CC + CD;

Solution to Exercise 2.34 (p. 29)This code was originally written by Bryson Hinton and then modi�ed:

cunit = zeros(1,150);

c0 = 45;

for n=1:150

%compute price for part A

if n >= 1 && n <= 4

ca=16;

elseif n >= 5 && n <= 24

ca=14;

elseif n >= 25 && n <= 99

ca=12.7;

else

ca=11;

end

%compute price for part B

if n >= 1 && n <= 9

cb=24.64;

elseif n >= 10 && n <= 49

cb=24.32;

elseif n >= 50 && n <= 99

cb=24.07;

else

cb=23.33;

end

%compute price for part C

if n >= 1 && n <= 24

cc=17.98;

elseif n >= 25 && n <= 49

cc=16.78;

45

else

cc=15.78;

end

%compute price for part D

if n >= 1 && n <= 9

cd=12.50;

elseif n >= 10 && n <= 99

cd=10.42;

else

cd=9.62;

end

%sum cost for all parts

cunit(n)= c0+ca+cb+cc+cd;

end

% Plot cost as a function of n

plot(1:150,cunit);

xlabel('n (units)');

ylabel('cost (dollars)');

title('Cost/unit as a function of number of units');

This code produces the plot in Figure 2.12.


0 50 100 150104

106

108

110

112

114

116

118

n (units)

cost

(do

llars

)Cost/unit as a function of number of units

Figure 2.12: Cost as a function of number of units produced.

Solution to Exercise 2.35 (p. 30)10 times.Solution to Exercise 2.36 (p. 31)This loop will continue to print 'Hello World' until the user stops the program. You can stop a program byholding down the 'Ctrl' key and simultaneously pressing the 'c' key.Solution to Exercise 2.37 (p. 31)

a =

1

a =

2

a =

4

a =

8

a =

16

a =

32

a =

47

64

a =

128


a =

1

a =

2

a =

6

a =

24

a =

120


APR = 14.9;

r = (1+APR/100)^(1/12)-1;


bn = 2203;

pn = max((r+0.01)*bn,10);


fn = r*bn;

bn = bn + fn - pn;

Solution to Exercise 2.42 (p. 32)This space intentionally left blank.Solution to Exercise 2.43 (p. 32)This space intentionally left blank.

48 BIBLIOGRAPHY

Bibliography

[1] Anthony M. Star�eld; Karl A. Smith; Andrew L. Bleloch. How To Model It: Problem Solving for the

Computer Age. Interaction Book Company, Edina, MN, 1994.

49

50 INDEX

Index of Keywords and Terms

Keywords are listed by the section with that keyword (page numbers are in parentheses). Keywordsdo not necessarily appear in the text of the page. They are merely associated with that section. Ex.apples, � 1.1 (1) Terms are referenced by the page they appear on. Ex. apples, 1

A Array, � 1.3(6)

B Basic operations, � 1.1(1)

C Credit Card, � 2.4.3(31)

E Engineering cost analysis, � 2.3.4(28)Engineering data analysis, � 2.2.4(20)Engineering modeling, � 2.2.3(19)Exercises, � 2.2.2(17), � 2.3.3(25), � 2.4.2(30)

F for loop, � 2.2.1(16), � 2.2.2(17), � 2.2.3(19),� 2.2.4(20)

G Graph, � 1.4(6)

I if statement, � 2.3.1(23), � 2.3.3(25),� 2.3.4(28)

L LabVIEW, � 1.2(4), � 1.3(6), � 1.4(6),� 2.1(15), � 2.2.1(16), � 2.2.2(17), � 2.2.3(19),� 2.2.4(20), � 2.3.1(23), � 2.3.2(24), � 2.3.3(25),� 2.3.4(28), � 2.4.1(30), � 2.4.2(30), � 2.4.3(31)

logical expression, � 2.3.2(24)logical operator, � 2.3.2(24)

M M-File, � 2.2.1(16), � 2.2.3(19), � 2.3.1(23),� 2.3.2(24), � 2.4.1(30)m-�les, � 2.1(15)MathScript, � 1.1(1), � 1.2(4), � 1.3(6),� 1.4(6), � 2.1(15), � 2.2.1(16), � 2.2.2(17),� 2.2.3(19), � 2.2.4(20), � 2.3.1(23), � 2.3.2(24),� 2.3.3(25), � 2.3.4(28), � 2.4.1(30), � 2.4.2(30),� 2.4.3(31)

P Personal Finance, � 2.4.3(31)Plot, � 1.4(6)Programming, � 2.1(15), � 2.2.1(16)

R relational operator, � 2.3.2(24)

V Variables, � 1.2(4)Vector, � 1.3(6)

W While Loop, � 2.4.2(30), � 2.4.3(31)While Loops, � 2.4.1(30)

ATTRIBUTIONS 51

Attributions

Collection: Introduction to LabVIEW MathScriptEdited by: Anthony Antonacci, Darryl MorrellURL: http://cnx.org/content/col10370/1.3/License: http://creativecommons.org/licenses/by/2.0/

Module: "Basic operations in LabVIEW MathScript"By: Anthony AntonacciURL: http://cnx.org/content/m13712/1.1/Pages: 1-4Copyright: Anthony AntonacciLicense: http://creativecommons.org/licenses/by/2.0/Based on: Basic operations in MATLABBy: Anders Gjendemsjø, Darryl MorrellURL: http://cnx.org/content/m13439/1.3/

Module: "Variables in LabVIEW MathScript"By: Anthony Antonacci, Darryl MorrellURL: http://cnx.org/content/m13726/1.2/Pages: 4-5Copyright: Anthony AntonacciLicense: http://creativecommons.org/licenses/by/2.0/Based on: Variables in MATLABBy: Darryl MorrellURL: http://cnx.org/content/m13354/1.2/

Module: "Vectors and Arrays in LabVIEW MathScript"By: Anthony Antonacci, Darryl MorrellURL: http://cnx.org/content/m13727/1.1/Page: 6Copyright: Anthony AntonacciLicense: http://creativecommons.org/licenses/by/2.0/Based on: Vectors and Arrays in MATLABBy: Darryl MorrellURL: http://cnx.org/content/m13355/1.1/

Module: "Graphical representation of data in LabVIEW MathScript"By: Anthony AntonacciURL: http://cnx.org/content/m13728/1.1/Pages: 6-12Copyright: Anthony AntonacciLicense: http://creativecommons.org/licenses/by/2.0/Based on: Graphical representation of data in MATLABBy: Anders GjendemsjøURL: http://cnx.org/content/m13252/1.1/

52 ATTRIBUTIONS

Module: "A Very Brief Introduction to Programming in LabVIEW MathScript"By: Anthony AntonacciURL: http://cnx.org/content/m13713/1.1/Page: 15Copyright: Anthony AntonacciLicense: http://creativecommons.org/licenses/by/2.0/Based on: A Very Brief Introduction to Programming in MATLABBy: Darryl MorrellURL: http://cnx.org/content/m13259/1.3/

Module: "Programming in LabVIEW MathScript-For Loops"By: Anthony Antonacci, Darryl MorrellURL: http://cnx.org/content/m13716/1.1/Pages: 16-17Copyright: Anthony AntonacciLicense: http://creativecommons.org/licenses/by/2.0/Based on: Programming in MATLAB-For LoopsBy: Darryl MorrellURL: http://cnx.org/content/m13258/1.3/

Module: "Programming in LabVIEW MathScript-Simple For Loop Exercises"By: Anthony Antonacci, Darryl MorrellURL: http://cnx.org/content/m13723/1.1/Pages: 17-19Copyright: Anthony AntonacciLicense: http://creativecommons.org/licenses/by/2.0/Based on: Programming in MATLAB-Simple For Loop ExercisesBy: Darryl MorrellURL: http://cnx.org/content/m13276/1.3/

Module: "Programming in LabVIEW MathScript-A Modeling Example Using For Loops"By: Anthony Antonacci, Darryl MorrellURL: http://cnx.org/content/m13717/1.1/Pages: 19-20Copyright: Anthony AntonacciLicense: http://creativecommons.org/licenses/by/2.0/Based on: Programming in MATLAB-A Modeling Example Using For LoopsBy: Darryl MorrellURL: http://cnx.org/content/m13275/1.2/

Module: "Programming in LabVIEW MathScript-A Data Analysis Example Using For Loops"By: Anthony Antonacci, Darryl MorrellURL: http://cnx.org/content/m13715/1.1/Pages: 20-23Copyright: Anthony AntonacciLicense: http://creativecommons.org/licenses/by/2.0/Based on: Programming in MATLAB-A Data Analysis Example Using For LoopsBy: Darryl MorrellURL: http://cnx.org/content/m13277/1.5/

ATTRIBUTIONS 53

Module: "Programming in LabVIEW MathScript-If Statements"By: Anthony Antonacci, Darryl MorrellURL: http://cnx.org/content/m13720/1.2/Pages: 23-24Copyright: Anthony AntonacciLicense: http://creativecommons.org/licenses/by/2.0/Based on: Programming in MATLAB-If StatementsBy: Darryl MorrellURL: http://cnx.org/content/m13356/1.2/

Module: "Programming in LabVIEW MathScript-Logical Expressions"By: Anthony Antonacci, Darryl MorrellURL: http://cnx.org/content/m13721/1.2/Pages: 24-25Copyright: Anthony AntonacciLicense: http://creativecommons.org/licenses/by/2.0/Based on: Programming in MATLAB-Logical ExpressionsBy: Darryl MorrellURL: http://cnx.org/content/m13357/1.4/

Module: "Programming in LabVIEW MathScript-Simple If Statement Exercises"By: Anthony Antonacci, Darryl MorrellURL: http://cnx.org/content/m13724/1.1/Pages: 25-28Copyright: Anthony AntonacciLicense: http://creativecommons.org/licenses/by/2.0/Based on: Programming in MATLAB-Simple If Statement ExercisesBy: Darryl MorrellURL: http://cnx.org/content/m13432/1.2/

Module: "Programming in LabVIEW MathScript-An Engineering Cost Analysis Example Using If State-ments"By: Anthony Antonacci, Darryl MorrellURL: http://cnx.org/content/m13719/1.1/Pages: 28-29Copyright: Anthony AntonacciLicense: http://creativecommons.org/licenses/by/2.0/Based on: Programming in MATLAB-An Engineering Cost Analysis Example Using If StatementsBy: Darryl MorrellURL: http://cnx.org/content/m13433/1.4/

Module: "Programming in LabVIEW MathScript-While Loops"By: Anthony Antonacci, Darryl MorrellURL: http://cnx.org/content/m13722/1.2/Page: 30Copyright: Anthony AntonacciLicense: http://creativecommons.org/licenses/by/2.0/Based on: Programming in MATLAB-While LoopsBy: Darryl MorrellURL: http://cnx.org/content/m13456/1.1/

54 ATTRIBUTIONS

Module: "Programming in LabVIEW MathScript-Simple While Loop Exercises"By: Anthony Antonacci, Darryl MorrellURL: http://cnx.org/content/m13725/1.1/Pages: 30-31Copyright: Anthony AntonacciLicense: http://creativecommons.org/licenses/by/2.0/Based on: Programming in MATLAB-Simple While Loop ExercisesBy: Darryl MorrellURL: http://cnx.org/content/m13457/1.2/

Module: "Programming in LabVIEW MathScript-A Personal Finance Example Using While Loops"By: Anthony Antonacci, Darryl MorrellURL: http://cnx.org/content/m13718/1.1/Pages: 31-32Copyright: Anthony AntonacciLicense: http://creativecommons.org/licenses/by/2.0/Based on: Programming in MATLAB-A Personal Finance Example Using While LoopsBy: Darryl MorrellURL: http://cnx.org/content/m13461/1.2/

Introduction to LabVIEW MathScriptThis course provides a brief introduction to LabVIEW MathScript, a textual math componenet of LabVIEWthat installs with LabVIEW 8.0 and newer versions. The modules for this course include typical syntax andprogramming methods commonly used when writing your own m-�le scripts. These MathScript moduleswere derrived from the course Freshman Engineering Applications of MATLAB, written by Professor DarrylMorrell.

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Introduction to LabVIEW Math Script