Chapter 2 (Part 2) MATLAB Basics - NJIT SOShung/cs101/chap02-2.pdfChapter 2 (Part 2) MATLAB Basics ....

dr.dcd.h CS 101 /SJC 5th Edition 1

Chapter 2 (Part 2) MATLAB Basics


Display Format

In the command window, integers are always displayed as integers

Characters are always displayed as strings

Other values are displayed using a specified display format

No matter what display format you choose, MATLAB uses double precision floating point values in its calculations


Display Format2

The display format can be changed by using format command

For example: format short

Default display format can be changed via the Preferences manually


Display Format2

The default format shows four digits after the decimal point, it is also known as short

format Descriptions Example

short 4 digits after decimal 3.1416

long 14 digits after decimal 3.141592653589793

short e 5 digits plus exponent 3.1416e+000

short g 5 digits plus w/ or w/o exponent 3.1416

long e 15 digits plus exponent 3.141592653589793e+000

long g 15 digits plus w/ or w/o exponent 3.14159265358979

bank dollars and cents format 3.14

hex 4-bit hexadecimal 400921fb54442d18

rat approximate ratio of small integers 355/113

compact approximate ratio of small integers

loose restore extra line feeds

+ only displays signs +


The disp Function

The disp function displays the contents of a numerical matrix or a string

The general form of disp function

disp(variable)


The disp Function2

To represent report that contains numbers and string, the following converting functions can be used:

num2str: convert a number to a string

int2str: convert an integer to a string


The disp Function3

To include an apostrophe (’) in a string, you need to enter the apostrophe twice. It is easier to think the syntax contains two strings.

disp( ’I’’m what I am’ )


Formatted Output: fprintf

fprintf function displays one or more values together with related text and provides control over the way values are displayed.

The general form of fprintf function

fprintf(format, data)

format is a string describing the way the data is to be printed

data is one or more scalars or arrays


Formatted Output: fprintf2

The general form of disp function

fprintf(format, data)

format is a string describing the way the data is to be printed

data is one or more scalars or arrays

The format is a string containing text plus special conversion characters describing the format of the data



Common conversion characters:

%? Desired Results

%d display value as an integer

%e display value in exponential form

%f display value in floating-point form

%g display value in either floating-point or .exponential form, whichever is shorter

%s display value as a string

\n line feed, skip to a new line



A few fprintf examples:

Use double % to insert a percentage sign in an

fprintf statement.



Advanced formatting characters

Extra Format Character

Descriptions

+ display ’+’ sign if data is positive

– display data in a left-adjusted fashion

m display data in a field m-digits wide

m.N display data in a field m-digits wide, .including n-digits after the decimal point

0 replaces extra blanks by zeros

For example:

fprintf(’%07.2f\n’, 12.345) produces ’0012.35’



Display a string in different formats:



Display a number in different formats:


ASCII

ASCII stands for American Standard Code for Information Interchange. ASCII encodes 128 characters into 7-bits. They are digits 0 to 9, letters a to z and A to Z, punctuations, control codes, and a space.


ASCII2

The ASCII chart:


ASCII3

To include West European languages an additional bit is added, this 8-bit code is called the extended-ASCII code.


Data Files

The save command saves data from the current workspace into a disk file.

The general form of save function

save <–ascii> filename <var_list>

By default, the filename will be given the extension mat.

If no variables are specified, all variables in the workspace will be saved.

If option –ascii is used, the data will be saved in an ASCII file with the exponential form.


Data Files2


Data Files3

The file wsav01.mat can not be opened externally outside the MATLAB

The file wsav02 can be opened by edit function or notepad.

Note that when the –ascii option is used, information such as variable names and types will be lost.

ASCII code for ‘xyz’


Data Files4

The load command loads data from a disk file into the current workspace.

The general form of load function

load filename

load –mat filename.dat

If a MAT-file is loaded, all of the variables will be restored with the names and types.


Data Files5

Data having different column sizes should not be saved together if the –ascii option will be used.


Data Files6

The contents of an ASCII-file will be converted into an array having the same name as the file (w/o the extension).

Data having different column sizes should not be saved together if the –ascii option will be used.


Scalar Arithmetic Operations

Arithmetic Operation

Algebraic Form MATLAB Form

Addition a + b a + b

Subtraction a – b a – b

Multiplication a x b a * b

Division a b

a / b or b \ a

Exponentiation ab a ^ b

____

Note:

b\a is called the left division.

Parentheses may be used to group terms and the sub-expressions inside the parentheses are evaluated first.


Scalar Arithmetic Operations2

Parentheses may be used to group terms and the sub-expressions inside the parentheses are evaluated first.

For example:

2^(8+6/3) returns 1024

2^8+6/3 returns 258


Array & Matrix Operations Operation Syntax Descriptions

Array Addition a + b Array addition and matrix addition are identical.

Array Subtraction a – b Array subtraction and matrix subtraction are identical.

Array Multiplication a .* b Element-by-element multiplication of a and b : a(i,j)*b(i,j). Both a and b must be the same shape.

Matrix Multiplication a * b The no. of columns in a must equal the no. of rows in b.

Array Right Division a ./ b Element-by-element division of a and b: a(i,j)/b(i,j). Both arrays must be the same shape.

Array Left Division a .\ b Element-by-element division of a and b: b(i,j)/a(i,j). Both arrays must be the same shape.

Matrix Right Division a / b In MATLAB, it is defined by a*inv(b), where inv(b) is the inverse of b.

Matrix Left Division a \ b In MATLAB, it is defined by inv(a)*b, where inv(a) is the inverse of a.

Array Exponentiation a .^ b Element-by-element exponential of a and b: a(i,j)^b(i,j). Both a and b must be the same shape.

Element-by-element operation is performed on corresponding elements in the associated two arrays.


Array & Matrix Operations2

Array operation between two arrays:

Array multiplication:

Matrix multiplication:


Precedence of Arithmetic Operations

Precedence Descriptions

1 Perform calculations inside all parentheses, working from the innermost set to the outermost.

2 Perform all exponentials, working from left to right.

3 Perform all multiplications and divisions, working from left to right.

4 Perform all additions and subtractions, working from left to right.

Note:

a^b^c is not evaluated as but (a^b)^c.


Solutions of Linear Equations

Consider the following system of three equations with three unknowns:

3x + 2y – z = 10

–x + 3y + 2z = 5

x – y – z = –1

which can be expressed as

AX = B

where A= , B= and X= .

It can be solved for X using linear algebra. The solution is

X = A-1B =


Homework Assignment #4

Quiz 2.3

Page 51: 2, 3

Quiz 2.4

Page 58: 1, 2

This assignment is due by next week.

Late submission will be penalized.


Common MATLAB Functions

Mathmatical functions:

abs, min, max, mod, rem

cos, sin, tan

acos, asin, atan, atan2(y,x)

exp, log, log10, sqrt

Rounding functions

ceil, floor, round, fix

String conversion functions

char, double, int2str, num2str, str2num


Mathematical Functions

abs(x): returns |x| or the magnitude if x is a complex number.

[maximum, index]=max(x): returns the maximum value in array x and its index.

[minimum, index]=min(x): returns the minimum value in array x and its index.


Mathematical Functions2

Both mod(x,y) and rem(x,y) return the reminder after division.

The mod function produces a result that is either zero or has the same sign as the divisor.

The rem function produces a result that is either zero or has the same sign as the dividend.


Mathematical Functions3

atan2(y,x): returns over 4 quadrants of angle.


Rounding Functions

ceil(x): rounds x to the nearest integer towards .

fix(x): rounds x to the nearest integer towards 0.

floor(x): rounds x to the nearest integer towards –

round(x): rounds x to the nearest integer.


String Conversion Functions

char: converts numbers to a string.

double: converts an array of char to ASCII codes.

int2str: converts a number to an integer string.

num2str: converts a number to a string.

str2num: converts a string to a number.


Two-Dimensional Plots

The general form of plot function

plot(x, y)

y is a 1-1 function of x

When plot is execute, a figure window opens.

Title and axis labels can be added by

title(str)

xlabel(str)

ylabel(str)

Grid lines can be enabled/disable by

grid on/off


Two-Dimensional Plots2


Save Plots

The print command can be used to save a plot as an image from a M-script

print <option> filename

Valid options

–deps: monochrome encapsulated postscript ___ __ image

–depsc: color encapsulated postscript image

–djpeg: JPEG image

–dpng: portable network graphic image

–dtiff: compressed TIFF image


Save Plots2

Use File/Save As menu option on the Figure Window to save a graphical image.


Multiple Plots

1st method: plot two functions y1=f(x1) and y2=g(x2) at once

plot(x1, y1, x2, y2, …)

x1 and x2 can be defined over different ranges

For example:

f(x) = sin(2x)

The first derivation of f(x) = 2 cos(2x)

To plot them side-by-side for comparison


Multiple Plots2


Multiple Plots3

2nd method: plot y1 and y2 separately with hold function enabled

plot(x1, y1)

hold on: Retain current plot when adding new plots

plot(x2, y2)

hold off: next plot will clear up figure space first


Multiple Plots4


Graph Properties

You can change the appearance of your

plots by selecting user defined line styles

color

mark styles.

Legends can be added by

legend(str1, str2, …, <position>)

Position: Best – least conflict with the figure

NorthWest North NorthEast

West East

SouthWest South SouthEast


Graph Properties2

Line Style Indicator Marker Style Indicator Color Indicator

solid - point . blue b

dotted : circle o green g

dash-dot -. x-mark x red r

dashed -- plus + cyan c

(none) (no line) star * magenta m

square s yellow y

diamond d black k

triangle down v

triangle up ^

triangle left <

triangle right >

pentagram p

hexagram h


Specify Graph Property

plot(x, y, opstr)

Opstr combining line style, marker style, and color

For example: ’:ok’ indicates dotted line ’:’, circle marker ’o’, and black color ’k’.

legend(str_list, ’Location’, ’Best’)

Best – least conflict with the figure

All locations can be outside plot, eg. ’BestOutside’


Specify Graph Property2


Specify Graph Property3


Logarithmic Plots

A logarithmic scale (base 10) is useful if a variable ranges over many orders of magnitude, or data varies exponentially.

semilogy – uses a log10 scale on the y axis

semilogx – uses a log10 scale on the x axis

loglog – uses a log10 scale on both axes


Logarithmic Plots2


Logarithmic Plots3


Example 2.4

Figure below shows a voltage source V=120 Volt with an internal resistance RS of 50 W supplying a load of resistance of RL. Find the value of load resistance that will result in the maximum possible power being supplies by the source to the load. Plot the power supplied to the load as a function of RL.


Example 2.42

The power supplied to the load RL is given by

PL = I2 RL

where I is the current supplied to the load, it can be obtained by Ohm’s law

V

RS+RL

Procedures to perform the work:

Define an array of possible values for RL

Compute the current for each value of RL

Compute the supplied power for each value of RL

Plot the power supplied to the load for each value of RL

Determine the maximum power

_______


Example 2.43


Example 2.44


Homework Assignment #5

2.15 Exercises

Page 83: 2.1 - 2.8

This assignment is due by next week.

Late submission will be penalized.

Chapter 2 (Part 2) MATLAB Basics - NJIT SOShung/cs101/chap02-2.pdfChapter 2 (Part 2) MATLAB Basics ....

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