1. DREAM PLAN IDEA IMPLEMENTATION

2. 2 Present to: Amirkabir University of Technology (Tehran Polytechnic) & Semnan University Dr. Kourosh Kiani Email: kkiani2004@yahoo.comkkiani2004@yahoo.com Email: Kourosh.kiani@aut.ac.irKourosh.kiani@aut.ac.ir Web: www.kouroshkiani.comwww.kouroshkiani.com Introduction to Matlab

3. Training

4. >>3^2 - (5 + 4)/2 + 6*3 ans = 22.5000 >>ans^2 + sqrt(ans) ans = 510.9934 >>u = cos(10) u = -0.8391 >>v = sin(10) v = -0.5440 >>uˆ2 + vˆ2 ans = 1

5. >>solve('x^2 - 2*x - 4 = 0') ans = 1 - 5^(1/2) 5^(1/2) + 1 >>solve('x^2 - 4 = 0') ans = -2 2 >>solve('x^3 - 27 = 0') ans = 3 - 3/2 - 3^(1/2)*3/2*I - 3/2 + 3^(1/2)*3/2*I

6. >>[x, y] = solve('x^2 - y = 2', 'y - 2*x = 5') x = 2*2^(1/2) + 1 1 - 2*2^(1/2) y = 4*2^(1/2) + 7 7 - 4*2^(1/2) >>Z = [2,4,6,8] Z = 2 4 6 8 >>Y = [4 -3 5 -2 8 1] Y = 4 -3 5 -2 8 1

7. >>X = 1:9 X = 1 2 3 4 5 6 7 8 9 >>X = 0:2:10 X = 0 2 4 6 8 10 >>X(3) ans = 4

8. >>X = 0:2:10 X = 0 2 4 6 8 10 >>X’ ans = 0 2 4 6 8 10 >>X.^2 ans = 0 4 16 36 64 100

9. >>X = 0:2:10 X = 0 2 4 6 8 10 >>Y=-4 Y = -4 >> X.*Y ans = 0 -8 -16 -24 -32 -40

10. >> A = [1, 2, 3, 4; 5, 6, 7, 8; 9, 10, 11, 12] A = 1 2 3 4 5 6 7 8 9 10 11 12 >> A = [1 2 3 4; 5 6 7 8; 9 10 11 12] A = 1 2 3 4 5 6 7 8 9 10 11 12 >> [2 3] < [3 2] ans = 1 0

11. >> x = -2:2; x >= 0 ans = 0 0 1 1 1 >> x(x >= 0) ans = 0 1 2

12. >> a=magic(4) a = 16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1 >> b=sum(a) b = 34 34 34 34 >> diag(a) ans = 16 11 6 1

13. >> a=magic(4) a = 16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1 >> a(4,4)=1000 a = 16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1000

14. >> A = [2 7 4] A = 2 7 4 >> A = [2; 7; 4] A = 2 7 4

15. >> A = [2 7 4; 3 8 9] A = 2 7 4 3 8 9 >> B=[A A] B = 2 7 4 2 7 4 3 8 9 3 8 9

16. >> u = [ 1:3 ]' u = 1 2 3 >> v = [ u u ] v = 1 1 2 2 3 3

17. >> a=[1 2;3 4] a = 1 2 3 4 >> cat_a=[a, 2*a; 3*a, 4*a; 5*a, 6*a] cat_a = 1 2 2 4 3 4 6 8 3 6 4 8 9 12 12 16 5 10 6 12 15 20 18 24 >> a=[1 2;3 4] a = 1 2 3 4 >> cat_a=[a, 2*a; 3*a, 4*a; 5*a, 6*a] cat_a = 1 2 2 4 3 4 6 8 3 6 4 8 9 12 12 16 5 10 6 12 15 20 18 24 Use square brackets [ ] 4*a

18. >> A=magic(4) A = 16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1 >> A(4,4) ans = 1 >> A(4,1) ans = 4 >> A(3,3) ans = 6

19. >> x = [ -2 0 9 1 4 ] x = -2 0 9 1 4 >> x(1) ans = -2 >> x(5) ans = 4 >> x(8) ??? Attempted to access x(8); index out of bounds because numel(x)=5. >> x(-1) ??? Attempted to access x(-1); index must be a positive integer or logical.

20. >> Z=[1+i 2 1; 2+5i i 2] Z = 1.0000 + 1.0000i 2.0000 1.0000 2.0000 + 5.0000i 0 + 1.0000i 2.0000

21. >> A=magic(4) A = 16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1 >> A(1:2,3:4) ans = 3 13 10 8

22. >> A=magic(4) A = 16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1 >> A([2 3],[1 2]) ans = 5 11 9 7

23. >> A=magic(4) A = 16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1 >> B=A([3 2],[2 1]) B = 7 9 11 5

24. >> A=magic(4) A = 16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1 >> B=[A(3,2),A(3,1);A(2,2),A(2,1)] B = 7 9 11 5

25. >> A=magic(4) A = 16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1 >> A(1,:) ans = 16 2 3 13 >> B=A(1,:) B = 16 2 3 13

26. >> A=magic(4) A = 16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1 >> A(1:2,:) ans = 16 2 3 13 5 11 10 8 >> A([1 2],:) ans = 16 2 3 13 5 11 10 8

27. >> a = [100 200 300 400 500 600 700] a = 100 200 300 400 500 600 700 >> b = [3 5 6] b = 3 5 6 >> c = a(b) c = 300 500 600

28. >> A=magic(6) A = 35 1 6 26 19 24 3 32 7 21 23 25 31 9 2 22 27 20 8 28 33 17 10 15 30 5 34 12 14 16 4 36 29 13 18 11 >> B=A(1:2:5,3) B = 6 2 34

29. >> A=magic(6) A = 35 1 6 26 19 24 3 32 7 21 23 25 31 9 2 22 27 20 8 28 33 17 10 15 30 5 34 12 14 16 4 36 29 13 18 11 >> B = A(:, 2:3) B = 1 6 32 7 9 2 28 33 5 34 36 29

30. >> x(1:5) ans = -2 0 9 1 4 >> x([2 4]) ans = 0 1

31. >> X=[2 6 4 9 7] X = 2 6 4 9 7 >> X([5 3 2 4 1]) ans = 7 4 6 9 2

32. >> x = 1:2:10 x = 1 3 5 7 9 >> y = 0:0.1:0.5 y = 0 0.1000 0.2000 0.3000 0.4000 0.5000 >> C= 10:-1:2 C = 10 9 8 7 6 5 4 3 2

33. >> A=100:-7:50 A = Columns 1 through 5 100 93 86 79 72 Columns 6 through 8 65 58 51 >> B=0:pi/4:pi B = 0 355/452 355/226 1065/452 355/113

34. linspace(x1, x2) gives 100 evenly spaced values between x1 and x2 x = linspace(5,20); linspace(a,b,n) generate n equally spaced points between a and b x = linspace(a,b,n) >> x = linspace(5,20,8) x = 5.0000 7.1429 9.2857 11.4286 13.5714 15.7143 17.8571 20.0000

35. logspace(a,b,n) generates a logarithmically equally spaced row vector x = logspace(a,b,n) logspace(a,b) generates 50 logarithmically equally spaced points x = logspace(a,b) >> logspace(-4,2,7) ans = 0.0001 0.0010 0.0100 0.1000 1.0000 10.0000 100.0000

36. >> A = [1:3:15; linspace(0,1,5)] A = 1.0000 4.0000 7.0000 10.0000 13.0000 0 0.2500 0.5000 0.7500 1.0000 >> A = [(1:3:15)', linspace(0,1,5)'] A = 1.0000 0 4.0000 0.2500 7.0000 0.5000 10.0000 0.7500 13.0000 1.0000

37. >> eye(3) ans = 1 0 0 0 1 0 0 0 1 >> eye(4) ans = 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1

38. >> zeros(4) ans = 0 0 0 0 >> zeros(3,5) ans = 0 0 0 0 0 >> zeros(4,5) ans = 0 0 0 0 0

39. >> ones(4) ans = 1 1 1 1 >> ones(3,5) ans = 1 1 1 1 1 >> ones(2,5) ans = 1 1 1 1 1

40. rand: uniformly distributed random numbers. >>A = rand(3,5) A = 0.9501 0.4860 0.4565 0.4447 0.9218 0.2311 0.8913 0.0185 0.6154 0.7382 0.6068 0.7621 0.8214 0.7919 0.1763 randn: normally distributed random numbers. >>B = randn(3,5) B = -1.1465 -0.0376 -0.1867 2.1832 1.0668 1.1909 0.3273 0.7258 -0.1364 0.0593 1.1892 0.1746 -0.5883 0.1139 -0.0956

42. >> a=[1 2; 3 5] a = 1 2 3 5 >> b=[3 4; 7 5] b = 3 4 7 5 >> a.*b ans = 3 8 21 25 >> a=[1 2; 3 5] a = 1 2 3 5 >> b=[3 4; 7 5] b = 3 4 7 5 >> a*b ans = 17 14 44 37

43. >> A=[2 3 8 1] A = 2 3 8 1 >> B=[1 4 5 2] B = 1 4 5 2 >> C=A.*B C = 2 12 40 2 >> d=A./B d = 2.0000 0.7500 1.6000 0.5000 >> A=[2 3 8 1] A = 2 3 8 1 >> B=[1 4 5 2] B = 1 4 5 2 >> d=A.^3 d = 8 27 512 1 >> E=(3).^B E = 3 81 243 9

44. >> 3 < 4 ans = 1 >> 6 < 3 ans = 0 >> 5==5 ans = 1 >> 5==7 ans = 0 >> 3 ~= 4 ans = 1 >> 3 ~= 3 ans = 0 >> 6 > 5 ans = 1 >> 6 > 8 ans = 0

45. >> a=[1 2; 0 -1] a = 1 2 0 -1 >> a>1 ans = 0 1 0 0 >> a<0 ans = 0 0 0 1

46. >> a=4 a = 4 >> b=3 b = 3 >> ~(a==b) ans = 1 >> a=4 a = 4 >> b=3 b = 3 >> c=5 c = 5 >> (a<b) & (b<c) ans = 0

47. >> a=4 a = 4 >> b=3 b = 3 >> c=5 c = 5 >> (a>b) | (a>c) ans = 1 >> (a>b) | (b<c) ans = 1 >> x=1 x = 1 >> y= -1 y = >> x>0 & y>0 ans = 0 >> x>0 | y>0 ans = 1

48. >> u = [0 0 1 1 0 1]; >> v = [0 1 1 0 0 1]; >> u | v ans = 0 1 1 1 0 1 >> u & v ans = 0 0 1 0 0 1

49. >> A=magic(4) A = 16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1 >> max(A) ans = 16 14 15 13 >> min(A) ans = 4 2 3 1 >> A=magic(4) A = 16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1 >> mean(A) ans = 8.5000 8.5000 8.5000 8.5000 >> sum(A) ans = 34 34 34 34 >> prod(A) ans = 2880 2156 2700 1248

50. >> A=[1 2 3 4 5 6] A = 1 2 3 4 5 6 >> max(A) ans = 6 >> min(A) ans = 1 >> sum(A) ans = 21 >> prod(A) ans = 720 >> A=[8 7 4 3 2 1 9 8] A = 8 7 4 3 2 1 9 8 >> sort(A) ans = 1 2 3 4 7 8 8 9

51. >> A=[8 7 4 3 2 1 9 8] A = 8 7 4 3 2 1 9 8 >> size(A) ans = 1 8 >> length(A) ans = 8 >> z=sqrt(16) z = 4 >> A=[16 25 49 100 12] A = 16 25 49 100 12 >> B=sqrt(A) B = 4.0000 5.0000 7.0000 10.0000 3.4641

52. >> A=0/0 A = NaN >> B=1/0 B = Inf >> realmax ans = 1.7977e+308 >> C=2^realmax C = Inf >> Inf/Inf ans = NaN >> t = 1 + 2 + 3 +... 4+5+6+7+8+9 t = 45

53. >> s = 'abc' s = abc >> s(1) ans = a >> s( [ 1 2 ] ) = 'XX' s = XXc

54. >> A=double( 'abc xyz' ) A = 97 98 99 32 120 121 122 >> double( 'ABC XYZ' ) ans = 65 66 67 32 88 89 90 >> char( [ 72 101 108 108 111 33 ] ) ans = Hello!

55. >> s = char( 'my first string', 'my second string' ) s = my first string my second string >> size(s) ans = 2 16 >> size( deblank( s(1,:) ) ) ans = 1 15

56. ischar() : returns 1 for a character array >>ischar ( 'CS 111' ) ans = 1 isletter() : returns 1 for letters of the alphabet >>isletter( 'CS 111' ) ans = 1 1 0 0 0 0 isspace() : returns 1 for whitespace (blank, tab, new line) >>isspace( 'CS 111' ) ans = 0 0 1 0 0 0

57. >> 'a' < 'e' ans = 1 >> 'fate' == 'cake' ans = 0 1 0 1 >> 'fate' > 'cake' ans = 1 0 1 0

58. strcmp() : returns 1 if two strings are identical >>a = 'Bilkent'; >>strcmp( a, 'Bilkent' ) ans = 1 >>strcmp( 'Hello', 'hello' ) ans = 0 strcmpi() : returns 1 if two strings are identical ignoring case >>strcmpi( 'Hello', 'hello' ) ans = 1

59. >> str1='My first string' str1 = My first string >> findstr(str1,'first') ans = 4 >> strcmp(str1,'My') ans = 0

60. >> strncmp(str1,'My',2) ans = 1 >> str2='45.6' str2 = 45.6 >> str2num(str2) ans = 45.6000

61. >> str1 ='My first string' str1 = My first string >> str2 = '45.6' str2 = 45.6 >> strcat(str1,str2) ans = My first string45.6

62. Lowercase-to-uppercase >>a = upper( 'This is test 1!' ) a = THIS IS TEST 1! Uppercase-to-lowercase >>a = lower( 'This is test 1!' ) a = this is test 1!

63. findstr() : finds one string within another one >>test = 'This is a test!'; >>pos = findstr( test, 'is' ) pos = 3 6 >>pos = findstr( test, ' ' ) pos = 5 8 10

64. strrep() : replaces one string with another >>s1 = 'This is a good example'; >>s2 = strrep( s1, 'good', 'great' ) s2 = This is a great example

65. Recall num2str() for numeric-to-string conversion >>str = [ 'Plot for x = ' num2str( 10.3 ) ] str = Plot for x = 10.3 str2num() : converts strings containing numbers to numeric form >>x = str2num( '3.1415' ) x = 3.1415

66. >> format long e; >> pi ans = 3.141592653589793e+000 >> format short g; >> pi ans = 3.1416 >> format long g; >> pi ans = 3.14159265358979 >> format long e; >> pi ans = 3.141592653589793e+000 >> format short g; >> pi ans = 3.1416 >> format long g; >> pi ans = 3.14159265358979

67. >> format hex; >> pi ans = 400921fb54442d18 >> format bank; >> pi ans = 3.14 >> format +; >> pi ans = + >> format rat; >> pi ans = 355/113 >> a=magic(4) a = 16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1 >> format +; >> a a = ++++

68. >> A=rand(4) A = 0.2769 0.6948 0.4387 0.1869 0.0462 0.3171 0.3816 0.4898 0.0971 0.9502 0.7655 0.4456 0.8235 0.0344 0.7952 0.6463 >> format rat; >> A=rand(4) A = 659/929 302/461 1049/1093 1927/2565 1409/1867 655/4028 547/1607 388/1521 175/634 1078/9059 580/991 637/1259 365/537 457/917 438/1957 1287/1841

69. >> N = 10*rand(1,8) N = 5.3080 7.7917 9.3401 1.2991 5.6882 4.6939 0.1190 3.3712 >> N = fix(N) N = 5 7 9 1 5 4 0 3

70. >> A = [... 16.0 3.0 2.0 13.0 5.0 10.0 11.0 8.0 9.0 6.0 7.0 12.0 4.0 15.0 14.0 1.0 ] A = 16 3 2 13 5 10 11 8 9 6 7 12 4 15 14 1 >> B = [A A+32; A+48 A+16] B = 16 3 2 13 48 35 34 45 5 10 11 8 37 42 43 40 9 6 7 12 41 38 39 44 4 15 14 1 36 47 46 33 64 51 50 61 32 19 18 29 53 58 59 56 21 26 27 24 57 54 55 60 25 22 23 28 52 63 62 49 20 31 30 17

71. A = 16 3 2 13 5 10 11 8 9 6 7 12 4 15 14 1 >> X=A X = 16 3 2 13 5 10 11 8 9 6 7 12 4 15 14 1 >> X(:,2) = [] X = 16 2 13 5 11 8 9 7 12 4 14 1

72. Deleting Rows and Columns >> A=[1 5 9;4 3 2.5; 0.1 10 3i+1] A = 1.0000 5.0000 9.0000 4.0000 3.0000 2.5000 0.1000 10.0000 1.0000+3.0000i >> A(:,2)=[] A = 1.0000 9.0000 4.0000 2.5000 0.1000 1.0000 + 3.0000i >> A(2,2)=[] ??? Indexed empty matrix assignment is not allowed. >> A=[1 5 9;4 3 2.5; 0.1 10 3i+1] A = 1.0000 5.0000 9.0000 4.0000 3.0000 2.5000 0.1000 10.0000 1.0000+3.0000i >> A(:,2)=[] A = 1.0000 9.0000 4.0000 2.5000 0.1000 1.0000 + 3.0000i >> A(2,2)=[] ??? Indexed empty matrix assignment is not allowed.

73. >> A = [5.36; 7.01; [ ]; 9.44] A = 5.3600 7.0100 9.4400

74. >> v = [ 1 3, sqrt(5)] v = 1.0000 3.0000 2.2361 >> D = [1:5; 6:10; 11:2:20] D = 1 2 3 4 5 6 7 8 9 10 11 13 15 17 19 >> d = [-3 4 2], M = diag(d) d = -3 4 2 M = -3 0 0 0 4 0 0 0 2

75. >> J = [1:4; 5:8; 9:12; 20 0 5 4] J = 1 2 3 4 5 6 7 8 9 10 11 12 20 0 5 4 >> K = [ diag(1:4) J; J' zeros(4,4)] K = 1 0 0 0 1 2 3 4 0 2 0 0 5 6 7 8 0 0 3 0 9 10 11 12 0 0 0 4 20 0 5 4 1 5 9 20 0 0 0 0 2 6 10 0 0 0 0 0 3 7 11 5 0 0 0 0 4 8 12 4 0 0 0 0

76. >> F = [0 1 8 7; 3 -2 -4 2; 4 2 1 1] F = 0 1 8 7 3 -2 -4 2 4 2 1 1 >> diag(F) ans = 0 -2 1

77. The command spy(K) will produce a graphical display of the location of the nonzero entries in K (it will also give a value for nz|the number of nonzero entries) >> J = [1:4; 5:8; 9:12; 20 0 5 4] J = 1 2 3 4 5 6 7 8 9 10 11 12 20 0 5 4 >> K = [ diag(1:4) J; J' zeros(4,4)] K = 1 0 0 0 1 2 3 4 0 2 0 0 5 6 7 8 0 0 3 0 9 10 11 12 0 0 0 4 20 0 5 4 1 5 9 20 0 0 0 0 2 6 10 0 0 0 0 0 3 7 11 5 0 0 0 0 4 8 12 4 0 0 0 0 >> spy(K)

78. >> x = 0:0.1:0.5; >> y = 4*sin(3*x); >> u = 3*sin(4*x); >> w=[ x' y' u'] w = 0 0 0 0.1000 1.1821 1.1683 0.2000 2.2586 2.1521 0.3000 3.1333 2.7961 0.4000 3.7282 2.9987 0.5000 3.9900 2.7279

79. >> i = [1, 3, 5]; >> j = [2,3,4]; >> v = [10 11 12]; >> S = sparse (i,j,v) S = (1,2) 10 (3,3) 11 (5,4) 12 >> T = full(S) T = 0 10 0 0 0 0 0 0 0 0 11 0 0 0 0 0 0 0 0 12

80. >> x = 0:0.05:6; >> y = sin(pi*x); >> Y = (y>=0).*y; >> plot(x,y,':',x,Y,'-' )

81. >> x = pi*(-1:3) x = -3.1416 0 3.1416 6.2832 9.4248 >> round(x) ans = -3 0 3 6 9 >> fix(x) ans = -3 0 3 6 9 >> floor(x) ans = -4 0 3 6 9 >> x = pi*(-1:3) x = -3.1416 0 3.1416 6.2832 9.4248 >> ceil(x) ans = -3 0 4 7 10 >> sign(x) ans = -1 0 1 1 1 >> rem(x,3) ans = -0.1416 0 0.1416 0.2832 0.4248

82. >> A = [ -2 3 4 4; 0 5 -1 6; 6 8 0 1] A = -2 3 4 4 0 5 -1 6 6 8 0 1 >> k = find(A==0) k = 2 9 >> k = find(A==4) k = 7 10

83. >> A = [ -2 3 4 4; 0 5 -1 6; 6 8 0 1] A = -2 3 4 4 0 5 -1 6 6 8 0 1 >> n = find(A <= 0) n = 1 2 8 9 >> A(n) ans = -2 0 0

84. >> A=[1 2 3;4 5 6;7 8 9] A = 1 2 3 4 5 6 7 8 9 >> A(:) ans = 1 4 7 2 5 8 3 6 9

85. >> A = 3+2*i; % The number (3+2i) is saved to variable A. >> A A = 3.0000 + 2.0000i >> B = phase(A); % The phase angle of (3+2i) is saved to variable B. >> B B = 0.5880 >> C = real(A); % The real part of (3+2i) is saved to variable C. >> C C = 3 >> D = imag(A); % The imaginary part of (3+2i) is saved to variable D. >> D D = 2 >> E = abs(A); % The absolute value of (3+2i) is saved to variable E. >> E E = 3.6056

86. To represent the polynomial x3 - 2x - 5, save the coefficients in a matrix: >>p = [1 0 –2 –5] To factor the polynomial equation x3 - 6x2 +11x - 6 = 0, enter the coefficients into a matrix and use the roots() command: >> p = [1 -6 11 -6]; >> r = roots(p)' r = 3.0000 2.0000 1.0000

87. >> student.name = 'Clinton, Bill'; >> student.SSN = 123456789; >> student.homework = [10 10 7 9 10]; >> student.exam = [98 94]; >> student student = name: 'Clinton, Bill' SSN: 123456789 homework: [10 10 7 9 10] exam: [98 94] >> student(2).name = 'Bush, G. W.'; >> student(2).SSN = 987654321; >> student(2).homework = [4 6 7 3 0]; >> student(2).exam = [53 66]; >> student student = 1x2 struct array with fields: name SSN homework exam

88. >> k=struct('a',10,'b',4, 'c', 'kiani'); >> k k = a: 10 b: 4 c: 'kiani' >> k.a ans = 10 >> k.b ans = 4 >> k.c ans = kiani

89. >> kk=struct('name',{'kourosh' 'pantea' 'shain'}, 'age', {40, 17 70}, 'other',{[1 2 3 4] [4 5 6] [7 8 9]}); >> kk kk = 1x3 struct array with fields: name age other >> kk(1) ans = name: 'kourosh' age: 40 other: [1 2 3 4] >> kk(2) ans = name: 'pantea' age: 17 other: [4 5 6] >> kk(3) ans = name: 'shain' age: 70 other: [7 8 9]

90. >> A(1,1) = {15}; >> A(1,2) = {[1,2,3,4,5]}; >> A(2,1) = {'kiani'}; >> A(2,2) = {[1 0 0;0 1 0;0 0 1]}; >> A A = [ 15] [1x5 double] 'kiani' [3x3 double] >> celldisp(A) A{1,1} = 15 A{2,1} = kiani A{1,2} = 1 2 3 4 5 A{2,2} = 1 0 0 0 1 0 0 0 1 >> A{2,2} ans = 1 0 0 0 1 0 0 0 1

91. >>cellplot(A)

92. >> A={[1 4 5;3 5 7;5 6 7],'Kourosh kiani';4+6i,-pi:pi/4:pi}; >> A A = [3x3 double] 'Kourosh kiani' [4.0000 + 6.0000i] [1x9 double] >> A(:) ans = [3x3 double] [4.0000 + 6.0000i] 'Kourosh kiani' [1x9 double]

93. >> cellplot(A)

94. >> A{:} ans = 1 4 5 3 5 7 5 6 7 ans = 4.0000 + 6.0000i ans = Kourosh kiani ans = Columns 1 through 9 -3.1416 -2.3562 -1.5708 -0.7854 0 0.7854 1.5708 2.3562 3.1416

95. >> A{1}(:,:) ans = 1 4 5 3 5 7 5 6 7 >> A{2}(:,:) ans = 4.0000 + 6.0000i >> A{3}(:,:) ans = Kourosh kiani >> A{4}(:,:) ans = Columns 1 through 9 -3.1416 -2.3562 -1.5708 -0.7854 0 0.7854 1.5708 2.3562 3.1416

96. >> A{1}(:,:) ans = 1 4 5 3 5 7 5 6 7 >> A{1}(1,:) ans = 1 4 5 >> A{1}(2,2) ans = 5 >> A{3}(1,:) ans = Kourosh kiani >> A{3}(1,4) ans = r

97. >> A(:,:,1) =zeros(3,3) A = 0 0 0 >> A(:,:,2) =eye(3,3) A(:,:,1) = 0 0 0 A(:,:,2) = 1 0 0 0 1 0 0 0 1 >> A(:,:,3) =magic(3) A(:,:,1) = 0 0 0 A(:,:,2) = 1 0 0 0 1 0 0 0 1 A(:,:,3) = 8 1 6 3 5 7 4 9 2

98. >> A=[1 2 3;4 5 6;7 8 9] A = 1 2 3 4 5 6 7 8 9 >> B=flipdim(A,1) B = 7 8 9 4 5 6 1 2 3 >> B=flipdim(A,2) B = 3 2 1 6 5 4 9 8 7 flipdim flip array along a specified dimension When the value of dim is 1, the array is flipped row-wise down. When dim is 2, the array is flipped columnwise left to right

99. >> A=[1 2 3;4 5 6;7 8 9] A = 1 2 3 4 5 6 7 8 9 >> B=fliplr(A) B = 3 2 1 6 5 4 9 8 7

100. >> A=[1 2 3;4 5 6;7 8 9] A = 1 2 3 4 5 6 7 8 9 >> B=flipud(A) B = 7 8 9 4 5 6 1 2 3

101. >> A = reshape(1:15,5,3) A = 1 6 11 2 7 12 3 8 13 4 9 14 5 10 15 >> x=1:8 x = 1 2 3 4 5 6 7 8 >> C = reshape(x,2,4) C = 1 3 5 7 2 4 6 8

102. >> A=[3 4; 5 2] A = 3 4 5 2 >> B=[2 4; 3 5] B = 2 4 3 5 >> C=kron(A,B) C = 6 12 8 16 9 15 12 20 10 20 4 8 15 25 6 10 >> A=[3 4; 5 2] A = 3 4 5 2 >> B=[2 4; 3 5] B = 2 4 3 5 >> C=kron(B,A) C = 6 8 12 16 10 4 20 8 9 12 15 20 15 6 25 10

103. >> A=[1 2 0] A = 1 2 0 >> norm(A, 1) ans = 3 >> norm(A, 2) ans = 2.2361 >> norm(A, 3) ans = 2.0801 >> norm(A, inf) ans = 2 >> norm(A) ans = 2.2361 Vector and Mtrix Norms The p-norm of a vector x

104. >> A=[1 2 0] A = 1 2 0 >> B=[norm(A) norm(A,1) norm(A,2) norm(A,3) norm(A,100) norm(A,inf)] B = 2.2361 3.0000 2.2361 2.0801 2.0000 2.0000

105. >> C = fix(10*rand(3,2)) C = 9 1 4 4 8 9 >> B=[norm(C,1) norm(C) norm(C,inf)] B = 21.0000 15.2147 17.0000

106. A=LU >> A=magic(4) A = 16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1 >> [L U]=lu(A) L = 1.0000 0 0 0 0.3125 0.7685 1.0000 0 0.5625 0.4352 1.0000 1.0000 0.2500 1.0000 0 0 U = 16.0000 2.0000 3.0000 13.0000 0 13.5000 14.2500 -2.2500 0 0 -1.8889 5.6667 0 0 0 0.0000

107. QR Factorization A=QR >> A=[1 4 2;3 5 7;3 5 1] A = 1 4 2 3 5 7 3 5 1 >> [Q R]=qr(A) Q = -0.2294 0.9733 -0.0000 -0.6882 -0.1622 -0.7071 -0.6882 -0.1622 0.7071 R = -4.3589 -7.8001 -5.9648 0 2.2711 0.6489 0 0 -4.2426 >> Q'*Q ans = 1.0000 -0.0000 -0.0000 -0.0000 1.0000 -0.0000 -0.0000 -0.0000 1.0000

109. A = 2 3 -1 1 6 1 -1 -2 3 >> b=[9;21;-1] b = 9 21 >> inv(A) ans = 0.8333 -0.2917 0.3750 -0.1667 0.2083 -0.1250 0.1667 0.0417 0.3750 >> inv(A) ans = 0.8333 -0.2917 0.3750 -0.1667 0.2083 -0.1250 0.1667 0.0417 0.3750 >> inv(A)*b ans = 1 3 2

110. >> a=[1 2 3]; % inner product >> b=[2 3 4]; >> c=dot(a,b) c = 20 >> a=[1 2 3]; % cross product >> b=[2 3 4]; >> d= cross(a,b) d = -1 2 -1

111. >> f = inline('x^3 +x -1') f = Inline function: f(x) = x^3 +x -1 >> f(4) ans = 67 >> f(-2) ans = -11

112. >> f = inline('3*x.^2 -2*y', 'x', 'y'); >> f(2,3) ans = 6 >> f(3,3) ans = 21

113. >> f = inline('x^3 +x -1') f = Inline function: f(x) = x^3 +x -1 >> A=[1 2 3;4 5 6;7 8 9] A = 1 2 3 4 5 6 7 8 9 >> B=f(A) B = 468 577 686 1065 1309 1553 1662 2041 2420

114. >> x = -1:.4:1; y = 0:.4:4; >> [X,Y] = meshgrid(x,y) X = -1.0000 -0.6000 -0.2000 0.2000 0.6000 1.0000

115. Y = 0 0 0 0 0 0 0.4000 0.4000 0.4000 0.4000 0.4000 0.4000 0.8000 0.8000 0.8000 0.8000 0.8000 0.8000 1.2000 1.2000 1.2000 1.2000 1.2000 1.2000 1.6000 1.6000 1.6000 1.6000 1.6000 1.6000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.4000 2.4000 2.4000 2.4000 2.4000 2.4000 2.8000 2.8000 2.8000 2.8000 2.8000 2.8000 3.2000 3.2000 3.2000 3.2000 3.2000 3.2000 3.6000 3.6000 3.6000 3.6000 3.6000 3.6000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000

116. >> f = inline('10*x.^2 + y.^2', 'x', 'y') f = Inline function: f(x,y) = 10*x.^2 + y.^2 >> Z = f(X,Y) Z = 10.0000 3.6000 0.4000 0.4000 3.6000 10.0000 10.1600 3.7600 0.5600 0.5600 3.7600 10.1600 10.6400 4.2400 1.0400 1.0400 4.2400 10.6400 11.4400 5.0400 1.8400 1.8400 5.0400 11.4400 12.5600 6.1600 2.9600 2.9600 6.1600 12.5600 14.0000 7.6000 4.4000 4.4000 7.6000 14.0000 15.7600 9.3600 6.1600 6.1600 9.3600 15.7600 17.8400 11.4400 8.2400 8.2400 11.4400 17.8400 20.2400 13.8400 10.6400 10.6400 13.8400 20.2400 22.9600 16.5600 13.3600 13.3600 16.5600 22.9600 26.0000 19.6000 16.4000 16.4000 19.6000 26.0000

118. r1=0.5:0.1:4; r2=1:0.1:5; [X,Y] = meshgrid(r1,r2); z=1-(X-2).^2-(Y-3).^2; z=max(z,0); surf(r1, r2, z); figure(gcf)

119. r1=0.5:0.1:4; r2=1:0.1:5; [X,Y] = meshgrid(r1,r2); s=max(min(1-abs(X-2),1-abs(Y-3)),0) surf(r1, r2, z); figure(gcf)

120. Questions? Discussion? Suggestions ?