National Workshop on LaTeX and MATLAB for Beginners

Transcription

1 BITS Pilani Pilani Campus National Workshop on LaTeX and MATLAB for Beginners December, 2014 Partially Supported By: DST-Rajasthan

2 BITS Pilani Pilani Campus Lecture-9 (Dr. Trilok Mathur) Creation of M-files & Graphics in MATLAB

3 Solving a system of linear equation using rref(a) Obtaining eigenvalue and eigenvector of a Matrix LU Factorization Roots of a polynomial 3

4 4 Consider following system of linear equations: t z x t y x z y x which is equivalent to following matrix equation: b AX where A b t z y x X and

5 Enter coefficient matrix A = [ ; ; ], and b = [16;16;5] Now define augmented matrix C = [A,b] and obtain Row reduced echelon form (rref) of C: rref (C) Thus the solutions are: {(x, y, z, t) = (25-6k, 9k+34, k, 9): k is any real number} 5

6 Enter a matrix A = [2 1 0;-3, 8, 4;4, 2, -9] >> eig (A) >> [V, D] = eig (A) Here V is the matrix containing the eigenvectors of A as its columns. D is a matrix that contains the eigenvalue of A on its diagonal LU decomposition of a matrix >> [L, U] = lu (A) Here L is a lower triangular matrix and U is a upper triangular matrix such that L*U = A 6

7 Let f ( x) 3x 4 4x 3 2x 2 17x 10 In MATLAB a polynomial of degree n is a row vector of dimension (n+1) 1. Enter a vector: >> f = [ ] >> roots( f ) This command will return all the 4 roots of f as a column vector. 7

8 Operator Symbol Description AND & Returns 1 for every element location that is true (non zero) for both array, otherwise 0 OR Returns 1 for every element location that is true (nonzero), at least for one array, otherwise 0 NOT ~ Complement each element of the array XOR xor Returns 1 for every element location that is true (nonzero) in only one array, otherwise 0 8

9 Note: MATLAB consider any non-zero numeric value as 1 and use it as input for logical expressions 9

10 M-File Creation MATLAB if MATLAB for Plotting A Graph 10

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16 If you want that your M-File after execution, show the result on command window, use X = disp (variable_name) command. It will show the value stored in variable X in M-File on the command window. If you want to display a message in command window use disp ( This is a message ) 16

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18 If you want to take input from user in your program, use X = input ( Please enter the value- ) This will show the message Please enter the value- in command window After getting input from user it will be stored in X, that you can use in your program later at any point. 18

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20 if Execute statements if condition is true Syntax if expression Statements; end Description if expression, statements, end evaluates expression and, if the evaluation yields logical 1 (true) or a nonzero result, executes one or more MATLAB commands denoted here as statements. 20

21 expression is a MATLAB expression, usually consisting of variables or smaller expressions joined by relational operators (e.g., count < limit), or logical functions (e.g., isreal(a)). Simple expressions can be combined by logical operators (&&,, ~) into compound expressions. MATLAB evaluates compound expressions for if from left to right, adhering to operator precedence rules. Nested if statements must each be paired with a matching 21 end.

22 The if function can be used alone or with the else and elseif functions. When using elseif and/or else within an if statement, the general form of the statement is: if expression1 statements1 ; elseif expression2 statements2; else statements3; end 22

23 Try disp ('This is a program for Subtraction of two matrices- ') a = input ('Please enter first Matrix - ') b = input ('Please enter Second Matrix b - ') if (size (a) ==size (b)); x = a - b; disp ('The Subtraction of two matrices is- '); disp (x); else disp ('ERROR- MATRIX DIMENSIONS MUST MATCH') end 23

24 Notice!! 24

25 for Execute block of code specified number of times Syntax for x=initval : endval,/initval : stepval : endval, statements, end Description for repeatedly executes one or more MATLAB statements in a loop. 25

26 Loop counter variable x is initialized to value initval at the start of the first pass through the loop, and automatically increments by 1 each time through the loop. The program makes repeated passes through statements until either x has incremented to the value endval, or MATLAB encounters a break, or return instruction, thus forcing an immediately exit of the loop. 26

27 The scope of the for statement is always terminated with a matching end The values initval and endval must be real numbers or arrays of real numbers, or can also be calls to functions that return the same. For loop can be used in nested form (that is one for loop inside the scope of other). For loop can be used in combination of other loops also. 27

28 Lets Try disp ('This is a program for summation of n natural numbers starting from zero') n = input ('Please enter the value of n - '); X = 0; for i = 1 : n end X = X+i; disp ('The summation is') disp (X) 28

29 1. Introduction to Graph Components 2. Some Pre-Defined MATLAB Functions 3. Plotting 2D Graphs 4. Editing Graphs 5. Bar Graphs 6. Pie Charts 7. Multiple Graphs 29

30 1. Introduction to Graph Components 2. Some Pre-Defined MATLAB Functions 3. Plotting 2D Graphs 4. Editing Graphs 5. Bar Graphs 6. Pie Charts 7. Multiple Graphs 30

31 1 Cosine 1 Sine 1 cos(n/4) n 31

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34 Ticks on Y- Axis Box Title Legend Y-Axis Label on Y- Axis Data Points/ Marker Curve/Line X-Axis Label on X- Axis Ticks on X- Axis 34

35 Note: You can edit each of the component of the graph except DATA POINTS. You can edit graphs manually, as well as automatically in m-file while plotting it. You can edit graphs at later point of time using.fig file, opened in editor. 35

36 1. Introduction to Graph Components 2. Some Pre-Defined MATLAB Functions 3. Plotting 2D Graphs 4. Editing Graphs 5. Bar Graphs 6. Pie Charts 7. Multiple Graphs 36

37 Before starting with the graph plots; some functions which are defined with MATLAB are listed hereafter (in alphabetical order). Use of these functions are also defined. Go to help and read the syntax type of a particular function you intend to use. The classification of these function is: 37

38 Trigonometric Exponential Classification Use Trigonometric functions with results in radians or degrees Exponential, logarithm, power, and root functions Complex Rounding and Remainder Numbers with real and imaginary components, phase angles Rounding, modulus, and remainder Discrete Math Prime factors, factorials, permutations, rational fractions, least common multiple, greatest common divisor 38

39 Trigonometric acos Inverse cosine; result in radians acosd Inverse cosine; result in degrees acosh Inverse hyperbolic cosine acot Inverse cotangent; result in radians acotd Inverse cotangent; result in degrees acoth Inverse hyperbolic cotangent acsc Inverse cosecant; result in radians acscd Inverse cosecant; result in degrees acsch Inverse hyperbolic cosecant asec Inverse secant; result in radians 39

40 asecd Inverse secant; result in degrees asech Inverse hyperbolic secant asin Inverse sine; result in radians asind Inverse sine; result in degrees asinh Inverse hyperbolic sine atan Inverse tangent; result in radians atan2 Four-quadrant inverse tangent atand Inverse tangent; result in degrees atanh Inverse hyperbolic tangent cos Cosine of argument in radians cosd Cosine of argument in degrees cosh Hyperbolic cosine cot Cotangent of argument in radians 40

41 cotd Cotangent of argument in degrees coth Hyperbolic cotangent csc Cosecant of argument in radians cscd Cosecant of argument in degrees csch Hyperbolic cosecant hypot Square root of sum of squares sec Secant of argument in radians secd Secant of argument in degrees sech Hyperbolic secant sin Sine of argument in radians sind Sine of argument in degrees sinh Hyperbolic sine of argument in radians tan Tangent of argument in radians tand Tangent of argument in degrees tanh Hyperbolic tangent 41

42 Exponential exp Exponential log Natural logarithm log10 Common (base 10) logarithm log2 Base 2 logarithm and dissect floating-point numbers into exponent and mantissa nextpow2 Next higher power of 2 nthroot Real nth root of real numbers pow2 Base 2 power and scale floating-point numbers reallog Natural logarithm for nonnegative real arrays realpow Array power for real-only output realsqrt Square root for nonnegative real arrays sqrt Square root 42

43 Complex abs Absolute value and complex magnitude angle Phase angle complex Construct complex data from real and imaginary components conj Complex conjugate cplxpair Sort complex numbers into complex conjugate pairs i Imaginary unit imag Imaginary part of complex number isreal Check if input is real arrayjimaginary unit real Real part of complex number sign Signum function unwrap Correct phase angles to produce smoother phase plots 43

44 Rounding and Remainder ceil Round toward positive infinity fix Round toward zero floor Round toward negative infinity idivide Integer division with rounding option mod Modulus after division rem Remainder after division round Round to nearest integer 44

45 Discrete Math factor Prime factors factorial Factorial function gcd Greatest common divisor isprime Array elements that are prime numbers lcm Least common multiple nchoosek Binomial coefficient or all combinations perms All possible permutations primes Generate list of prime numbers rat, rats Rational fraction approximation 45

46 Polynomials conv Convolution and polynomial multiplication deconv De-convolution and polynomial division poly Polynomial with specified roots polyder Polynomial derivative polyeig Polynomial eigenvalue problem polyfit Polynomial curve fitting polyint Integrate polynomial analytically polyval Polynomial evaluation polyvalm Matrix polynomial evaluation roots Polynomial roots 46

47 1. Introduction to Graph Components 2. Some Pre-Defined MATLAB Functions 3. Plotting 2D Graphs 4. Editing Graphs 5. Bar Graphs 6. Pie Charts 7. Multiple Graphs 47

48 The simplest way of plotting a 2D graph in MATLAB is via using function: Plot (A) Plot (A, B) Description: plot(a) plots the columns of A versus their index. plot(a, B) plots the columns of A versus the columns of B. 48

49 x=0:0.1:10; A = cos (x) plot(x, A) 49

50 1. Introduction to Graph Components 2. Some Pre-Defined MATLAB Functions 3. Plotting 2D Graphs 4. Editing Graphs 5. Bar Graphs 6. Pie Charts 7. Multiple Graphs 50

51 Y = [ ] plot (Y) Y = [ ] X = [ ] plot (X, Y) 51

52 Changing the color of the graph: R = [ ] S = [ ] plot (R, S, 'k') R = [ ] S = [ ] plot (R, S, 'b') 52

53 The various color codes are available with MATLAB, which are listed in HELP Few of them are Cyan - c Red - r Magenta - m Yellow- y 53

54 Plotting Data Points Only: R = [ ] S = [ ] plot (R, S, '*b') The other symbols are + for plus symbol O for Circle > for Triangle < for Triangle s for square d for Dimond p for pantagon 54

55 Plotting Data Points with Line : R = [ ] S = [ ] plot (R, S, '-square') 55

56 Defining Line Width: R = [ ] S = [ ] plot (R, S, '-m', 'LineWidth', 12) 56

57 Defining Marker Size: R = [ ] S = [ ] plot (R, S, '->m', 'MarkerSize', 12) 57

58 Defining Marker Color: R = [ ] S = [ ] plot (R, S, '->m', 'MarkerFaceColor', 'b') 58

59 Defining Multiple Properties: R = [ ] S = [ ] plot (R, S, ' <b','linewidth',3,'markerfacecolor','m', 'MarkerSize', 24); 59

60 Defining Axes in Graph: axis([xmin xmax ymin ymax]) x = -pi:.1:pi; y = sin(x); plot (x,y) x = -pi:.1:pi; y = sin(x); plot(x,y) axis([ ]); 60

61 Defining Ticks on X- Axis and Y-Axis in Graph: y = sin(x); plot(x,y) set(gca,'xtick',-pi:pi/2:pi) gca: command to handle current axis set(h, Propertyname, propertyvalue, ) 61

62 Defining Ticks Label on X- Axis and Y-Axis in Graph: x = -pi:.1:pi; y = sin(x); plot(x,y) set(gca,'xtick',-pi:pi/2:pi) set(gca,'xticklabel',{'-pi','- pi/2','0','pi/2','pi'}) 62

63 Defining Ticks Label on X- Axis and Y-Axis in Graph: x = -pi:.1:pi; y = sin(x); plot(x,y) set(gca,'xtick',-pi:pi/2:pi) set(gca,'xticklabel',{'-pi','- pi/2','0','pi/2','pi'}) xlabel('-\pi \leq \Theta \leq \pi') ylabel('sin(\theta) ) 63

64 Defining Title and Text in Graph: x = -pi:.1:pi; y = sin(x); plot(x,y) set(gca,'xtick',-pi:pi/2:pi) set(gca,'xticklabel',{'-pi','- pi/2','0','pi/2','pi'}) xlabel('-\pi \leq \Theta \leq \pi') ylabel('sin(\theta)') title('plot of sin(\theta) ) 64

65 Defining Legend in Graph: X = [ ]; Y1 = [ ]; plot(x,y1,'-sb','markeredgecolor','k'); axis([ ]); set(gca,'xtick',[ ]); set(gca,'xticklabel',{'0' '200' '400' '600' '800' '1000' '1200' '1400'}); set(gca,'ytick',[ ]); set(gca,'yticklabel',{'500', '1000','1500','2000','2500','3000'}); xlabel('total Number of Request Made for Connection Establishment/Time '); ylabel('success Rate for Connection Establishment (SCER)'); legend('v-tft'); Title('Comparison'); 65

66 1. Introduction to Graph Components 2. Some Pre-Defined MATLAB Functions 3. Plotting 2D Graphs 4. Editing Graphs 5. Bar Graphs 6. Pie Charts 7. Multiple Graphs 8. Sub-graph 9. Demo: On Graph Generation 66

67 Bar Graph: bar(y) bar(x,y) bar(...,width) bar(...,'style') bar(...,'bar_color') bar(...,'propertyname',propertyvalue,...) 67

68 A bar graph displays the values in a vector or matrix as horizontal or vertical bars. bar(y) draws one bar for each element in Y. If Y is a matrix, bar groups the bars produced by the elements in each row. The x-axis scale ranges from 1 up to length(y) when Y is a vector, and 1 to size(y,1), which is the number of rows, when Y is a matrix. The default is to scale the x-axis to the highest x-tick on the plot, (a multiple of 10, 100, etc.). 68

69 Y =magic(4)*10; bar(y) 69

70 X=[1:10]; Y=rand(10,1); bar(x,y,'r'); xlabel('x','fontsize',18); Note: Editing of bar is similar to that of plot 70

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72 1. Introduction to Graph Components 2. Some Pre-Defined MATLAB Functions 3. Plotting 2D Graphs 4. Editing Graphs 5. Bar Graphs 6. Pie Charts 7. Multiple Graphs 72

73 Pie Chart pie(x) pie(x,explode) pie(...,labels) Description pie(x) draws a pie chart using the data in X. Each element in X is represented as a slice in the pie chart. pie(x,explode) offsets a slice from the pie. Explode is a vector or matrix of zeros and nonzeros that correspond to X. Explode must be the same size as X. pie(...,labels) specifies text labels for the slices. The number of labels must equal the number of elements in X. 73

74 Try: x = [ ] pie(x) 74

75 Try: x = [ ] explode = [ ]; pie(x,explode) 75

76 Try: pie(1:3,{'taxes','expenses','profit'}) 76

77 Try: x = [ ]; pie(x) 77

78 Try: X = [ ]; Explode = [ ]; Pie(X, Explode) 78

79 1. Introduction to Graph Components 2. Some Pre-Defined MATLAB Functions 3. Plotting 2D Graphs 4. Editing Graphs 5. Bar Graphs 6. Pie Charts 7. Multiple Graphs 79

80 Suppose you need to analyze more than one variable in a single graph That is, you need different curves/plots in a single run of your program on one plot for such case you can use following syntax: hold on; plot (X,Y) hold off; 80

81 Try: X = [ ] Y = [ ] Z = [ ] hold on; plot (X, Y, '-or') plot (Y,Z, '-*c') hold off; 81

82 Try: X = [ ] Y = [ ] Z = [ ] figure; hold on; plot (X,Y, '-or') plot (Y,Z, '-*c') hold off; figure; plot (X,Z, '-sm') 82

83 To save figure in current directory: saveas ( filename ) % by default as fig file saveas ( filename.jpg ) saveas ( filename.tif ) saveas is also used for other type of files, such as.pdf. 83

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