Chapter 2 (Part 2) MATLAB Basics. dr.dcd.h CS 101 /SJC 5th Edition 1
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1 Chapter 2 (Part 2) MATLAB Basics dr.dcd.h CS 101 /SJC 5th Edition 1
2 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 dr.dcd.h CS 101 /SJC 5th Edition 2
3 Display Format 2 The display format can be changed by using format command For example: format short Default display format can be changed via the Preferences manually dr.dcd.h CS 101 /SJC 5th Edition 3
4 Display Format 2 The default format shows four digits after the decimal point, it is also known as short format Descriptions Example short 4 digits after decimal long 14 digits after decimal short e 5 digits plus exponent e+000 short g 5 digits plus w/ or w/o exponent long e 15 digits plus exponent e+000 long g 15 digits plus w/ or w/o exponent bank dollars and cents format 3.14 hex 4-bit hexadecimal fb54442d18 rat approximate ratio of small integers 355/113 compact loose approximate ratio of small integers restore extra line feeds + only displays signs + dr.dcd.h CS 101 /SJC 5th Edition 4
5 The disp Function The disp function displays the contents of a numerical matrix or a string The general form of disp function disp(variable) dr.dcd.h CS 101 /SJC 5th Edition 5
6 The disp Function 2 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 dr.dcd.h CS 101 /SJC 5th Edition 6
7 The disp Function 3 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 ) dr.dcd.h CS 101 /SJC 5th Edition 7
8 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 dr.dcd.h CS 101 /SJC 5th Edition 8
9 Formatted Output: fprintf 2 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 dr.dcd.h CS 101 /SJC 5th Edition 9
10 Formatted Output: fprintf 3 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 dr.dcd.h CS 101 /SJC 5th Edition 10
11 Formatted Output: fprintf 4 A few fprintf examples: Use double % to insert a percentage sign in an fprintf statement. dr.dcd.h CS 101 /SJC 5th Edition 11
12 Formatted Output: fprintf 5 Advanced formatting characters Extra Format Character Descriptions + display + sign if data is positive display data in a left-adjusted fashion m m.n display data in a field m-digits wide 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, ) produces dr.dcd.h CS 101 /SJC 5th Edition 12
13 Formatted Output: fprintf 6 Display a string in different formats: dr.dcd.h CS 101 /SJC 5th Edition 13
14 Formatted Output: fprintf 7 Display a number in different formats: dr.dcd.h CS 101 /SJC 5th Edition 14
15 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. dr.dcd.h CS 101 /SJC 5th Edition 15
16 ASCII 2 The ASCII chart: dr.dcd.h CS 101 /SJC 5th Edition 16
17 ASCII 3 To include West European languages an additional bit is added, this 8-bit code is called the extended-ascii code. dr.dcd.h CS 101 /SJC 5th Edition 17
18 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. dr.dcd.h CS 101 /SJC 5th Edition 18
19 Data Files 2 dr.dcd.h CS 101 /SJC 5th Edition 19
20 Data Files 3 The file wsav01.mat can not be opened externally outside the MATLAB The file wsav02 can be opened by edit function or notepad. ASCII code for xyz Note that when the ascii option is used, information such as variable names and types will be lost. dr.dcd.h CS 101 /SJC 5th Edition 20
21 Data Files 4 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. dr.dcd.h CS 101 /SJC 5th Edition 21
22 Data Files 5 Data having different column sizes should not be saved together if the ascii option will be used. dr.dcd.h CS 101 /SJC 5th Edition 22
23 Data Files 6 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. dr.dcd.h CS 101 /SJC 5th Edition 23
24 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 a b a ^ b Note: b\a is called the left division. Parentheses may be used to group terms and the subexpressions inside the parentheses are evaluated first. dr.dcd.h CS 101 /SJC 5th Edition 24
25 Scalar Arithmetic Operations 2 Parentheses may be used to group terms and the sub-expressions inside the parentheses are evaluated first. For example: 2^(8+6/3) returns ^8+6/3 returns 258 dr.dcd.h CS 101 /SJC 5th Edition 25
26 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 Array Left Division Matrix Right Division Matrix Left Division Array Exponentiation a./ b a.\ b a / b a \ b a.^ b Element-by-element division of a and b: a(i,j)/b(i,j). Both arrays must be the same shape. Element-by-element division of a and b: b(i,j)/a(i,j). Both arrays must be the same shape. In MATLAB, it is defined by a*inv(b), where inv(b) is the inverse of b. In MATLAB, it is defined by inv(a)*b, where inv(a) is the inverse of a. 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. dr.dcd.h CS 101 /SJC 5th Edition 26
27 Array & Matrix Operations 2 Array operation between two arrays: Array multiplication: Matrix multiplication: dr.dcd.h CS 101 /SJC 5th Edition 27
28 Precedence of Arithmetic Operations Precedence Descriptions Perform calculations inside all parentheses, working from the innermost set to the outermost. Perform all exponentials, working from left to right. Perform all multiplications and divisions, working from left to right. Perform all additions and subtractions, working from left to right. Note: a^b^c is not evaluated as but (a^b)^c. dr.dcd.h CS 101 /SJC 5th Edition 28
29 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 -1 B = dr.dcd.h CS 101 /SJC 5th Edition 29
30 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. dr.dcd.h CS 101 /SJC 5th Edition 30
31 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 dr.dcd.h CS 101 /SJC 5th Edition 31
32 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. dr.dcd.h CS 101 /SJC 5th Edition 32
33 Mathematical Functions 2 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. dr.dcd.h CS 101 /SJC 5th Edition 33
34 Mathematical Functions 3 atan2(y,x): returns over 4 quadrants of angle. dr.dcd.h CS 101 /SJC 5th Edition 34
35 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. dr.dcd.h CS 101 /SJC 5th Edition 35
36 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. dr.dcd.h CS 101 /SJC 5th Edition 36
37 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 dr.dcd.h CS 101 /SJC 5th Edition 37
38 Two-Dimensional Plots 2 dr.dcd.h CS 101 /SJC 5th Edition 38
39 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 dr.dcd.h CS 101 /SJC 5th Edition 39
40 Save Plots 2 Use File/Save As menu option on the Figure Window to save a graphical image. dr.dcd.h CS 101 /SJC 5th Edition 40
41 Multiple Plots 1st method: plot two functions y 1 =f(x 1 ) and y 2 =g(x 2 ) at once plot(x 1, y 1, x 2, y 2, ) x 1 and x 2 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 dr.dcd.h CS 101 /SJC 5th Edition 41
42 Multiple Plots 2 dr.dcd.h CS 101 /SJC 5th Edition 42
43 Multiple Plots 3 2nd method: plot y 1 and y 2 separately with hold function enabled plot(x 1, y 1 ) hold on: Retain current plot when adding new plots plot(x 2, y 2 ) hold off: next plot will clear up figure space first dr.dcd.h CS 101 /SJC 5th Edition 43
44 Multiple Plots 4 dr.dcd.h CS 101 /SJC 5th Edition 44
45 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 dr.dcd.h CS 101 /SJC 5th Edition 45
46 Graph Properties 2 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 triangle up v ^ triangle left < triangle right > pentagram hexagram p h dr.dcd.h CS 101 /SJC 5th Edition 46
47 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 dr.dcd.h CS 101 /SJC 5th Edition 47
48 Specify Graph Property 2 dr.dcd.h CS 101 /SJC 5th Edition 48
49 Specify Graph Property 3 dr.dcd.h CS 101 /SJC 5th Edition 49
50 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 dr.dcd.h CS 101 /SJC 5th Edition 50
51 Logarithmic Plots 2 dr.dcd.h CS 101 /SJC 5th Edition 51
52 Logarithmic Plots 3 dr.dcd.h CS 101 /SJC 5th Edition 52
53 Example 2.4 Figure below shows a voltage source V=120 Volt with an internal resistance R S of 50 W supplying a load of resistance of R L. 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 R L. dr.dcd.h CS 101 /SJC 5th Edition 53
54 Example The power supplied to the load R L is given by P L = I 2 R L where I is the current supplied to the load, it can be obtained by Ohm s law V R S +R L Procedures to perform the work: Define an array of possible values for R L Compute the current for each value of R L Compute the supplied power for each value of R L Plot the power supplied to the load for each value of R L Determine the maximum power dr.dcd.h CS 101 /SJC 5th Edition 54
55 Example dr.dcd.h CS 101 /SJC 5th Edition 55
56 Example dr.dcd.h CS 101 /SJC 5th Edition 56
57 Homework Assignment # Exercises Page 83: This assignment is due by next week. Late submission will be penalized. dr.dcd.h CS 101 /SJC 5th Edition 57
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